I feel like I'm the only poster in this thread who wasn't born in the mid 90s or later and who has owned consoles not produced by Nintendo... Most of these are repeats already, but with good reason. Roughly in the order in which I first played them. Will probably edit the writing in the morning because I think I'm too tired to have written this coherently. Stealing the hell out of pictures already used so I don't have to find my own !
Chrono Trigger
I believe this was the first game I played that I would still consider a great game. There's a few I loved when I first played them that don't appeal to me anymore as an adult, but I still think Chrono Trigger is one of the best RPGs on my time(a genre this list will have an obvious bias toward). It's not the RPG with the most depth or the best mechanics but it has more charm than almost any other game I've ever played. The story is compelling in spite of its simplicty, the characters are likable, and all the little things in the game are done well to keep you immersed and interested. Great soundtrack, too. The best of a great generation of RPGs, though it aged a lot better than most of its generational siblings.
Dragon Warrior Monsters
I'm not necessarily disappointed in the way history played out and the fact I wound up an administrator at a Pokemon forum or anything, but Pokemon games, while addictive, innovative, and amazing at creating communities and connecting people(which led to its success relative to competitors) were pretty much the worst monster games made.
Dragon Warrior Monsters was the most obvious spin-off monster game attempting to bite at that, given its release date, but it had some unique gameplay options that made it the best of its subgenre. The breeding system in this game was fantastic, leading to a tangible reward from breeding several generations of monsters to get the rarest, most powerful breeds of monsters(not to mention getting the best moves on them) that the ridiculousness of breeding in Pokemon with its hidden IVs and static species couldn't hope to match. The gameplay was simple and repetitive given the massive amount of randomly generated maps in the game, but the process of breeding massive trees of monsters to end up with the good stuff almost singlehandedly made this game the best of the series. There was some fun in hunting monsters down and trying to lure them with meat and the general exploration element(as well as being able to poach monsters from other breeders met in the wild), and some of the games bosses actually provided a reasonable challenge, something Pokemon and Digimon never matched very well.
Busy, busy, busy...
Monster Rancher 2
Like DWM, a game I''ve probably spent 400 or 500 hours with over the years. I actually bought my Playstation for this game as a kid because my neighbor was too much of a wimp to take his MR2 disc out and replace it with a different CD to get info to generate his monsters(which is the monster generation technique of the game) because he was worried it'd ruin his PSX or something, so I bought my own to prove the point. I haven't changed much over the years, I guess.
If I hadn't bought any PSX games after MR2 I think it would have been worth the money. I think this probably gets the title for my favorite game ever. Unlike the other monster games, which were RPG focused, MR2 is a monster raising simulator/strategy game where you tend to only have indirect control of the results(outside of battle, which has an auto mode I wouldn't suggest). Breeding monsters is pretty interesting in a way unique to MR, since monsters have a main breed and a subbreed (like Mocchi/Mocchi is a pure breed, but it could be part Suezo, which would be Mocchi/Suezo, which would make it look like a Mocchi in shape with Suezo-like-traits), and each subbreed would influence the resource regeneration, lifespan, and stats of the monster in question(the breeding system more or less works accurately as far as how alleles work IRL). The amount of variables that influences how strong your monster eventually got like managing tiredness, stress, hunger, training, exploration, and tournaments and the effects they have on the monster's lifespan was really engaging and combat tended to be reasonably challenging if you weren't horrifically overleveled for the class you were in. The Big 4 and the challenge events at the end of the game were surprisingly difficult and made me really work to beat the game as a kid. There's actually still a few monsters I've never had the chance to raise in spite of all the time I've spent with it, which I think says a lot for the game's depth. I can beat the game on one monster now after playing it so much over the years, but still usually do so once every summer or so because it's still amazing after so long. It's too bad this series didn't get more popular in the US, I think a lot of people would have really enjoyed it. Later entries in the series fell off a lot, but the two GBA titles were both excellent(especially the 2nd).
Boasts the most hilarious translation of any game I've ever seen. It's not like, Zero Wing, or whatever, but it's hilariously charming, especially later in the game when you can tell the translators pretty much just gave up. Some of the things the characters say throughout the game are just hilariously ridiculous. The best scene is definitely a really rare one that involves aliens landing, which unlocks Metalner for the player, which is just completely illogically written. I was playing it one summer at Psycho's apartment with his GF at the time and one of our other friends around and we were reading the dialogue of the game like a play for comedic effect and we pretty much completely lost it during that section because of how little sense it made. Lots of "..wait, what?"s.
Digimon World 1
I'm not quite as passionate about this one as the previous two monster games, and this one might not even objectively be better than Pokemon, but I liked it a lot more than any of the individual Pokemon games, anyway. Early in the game, balancing training with exploration and getting the right digivolutions(or in the case of most Ultimates, getting any digivolutions at all) was challenging and fun, and not having direct control of combat kept the game challenging even when it really shouldn't have been. The difficulty of raising a powerful monster nosedives as you get more resources(having enough gold to always use training boosting foods and the training manual is gamebreaking before you even factor in that you can basically get infinite chips by abusing some bad game mechanics and glitches), but the game remains charming enough that it's fun to finish, mostly. Horribly mistranslated, but in a lazy way rather than a funny way.
Pokemon Snap
The most fun game in the franchise. Sure, it didn't test my strategic mind or my reflexes or whatever but it was charming and the sticker station thing at Blockbuster was awesome. Bought this again for my virtual console a month or so ago and it was totally worth it. Has a special place in my heart for being one of the first games I remember completing 100% without any help from the internet or a strategy guide.
Metal Gear Solid
I don't think I really understood what storytelling in videogames was going to be capable of until this game. I actually really hate the gameplay in this series -- while I would objectively call the gameplay good, it just doesn't fit my tastes in genre -- but I suffer through it because the storytelling is amazing. It's one series where I'd really just be happier if it was a movie or a TV show or something, but it isn't, and it's been worth my money every time. MGS1 was one of the first games with full voice acting and it made an excellent script seem far more alive than any other game I'd played to that point. The soundtrack added a lot to it, and it just felt dramatic and terrifying in a way I hadn't seen in a game before. Snake, Naomi, Campbell, and Meryl are pretty fantastic characters that it became easy to care about. The humor is probably the high point of the game, as well as the series... stuff like Psycho Mantis reading your memory card (and that boss fight in general, which is my favorite in any video game ever) makes MGS stand out.
Final Fantasy Tactics
There was a time when this was as or more popular with the group that eventually created this site than Pokemon itself. I dare say if there was multiplayer FFT there wouldn't be a website for me to be writing this on myself. I kinda picked it up from them, and am glad I did. Another horrifically translated game (wait, where's Dycedarg's Elder Brother?), but it the difficulty was pretty challenging the first playthrough(as long as you don't use Orlandu!) and SCCs and such kept it fun on repeats. Surprisingly good plot with the war of the lions and the backstabbing and all of that noise. Some great characters in Delita, Zalbag, Wiegraf, Agrias, etc. Another one of those games I can play through basically an infinite amount of times.
Chrono Cross
I really hated this game the first time I played through it because it wasn't the sequel I wanted for Chrono Trigger, but I warmed up to it over time. It's a fantastic game in its own right, with one of the most complex plots an RPG has ever seen(though it presents it ambiguously enough that it's almost impossible to piece together without outside help... there's a FAQ about it on GameFAQs that I think is nearly as long as the game script). There's a few too many characters, but the alternate dimensions thing allowed for some neat writing opportunities showing different ways characters' fates could have changed as well as some major ones with that region of the world itself. Some really fantastic characters in Harle and Kid, which make me wish the game had focused more on developing fewer characters given how well they did with what they bothered to develop. Some of the more emotional RPG moments with the flashback to the burning orphanage and the fight with Miguel set the game over the top. Also has my favorite video game soundtrack of all time.
Sonic Adventure 2
OK, I'm really straining my credibility with this one but since this was "favorite" rather than "best" I feel good listing this. I totally hear people who complain that Sonic was always way better in 2D, but I only had a SNES in that era of gaming and I had a fantastic time with Sonic on the Dreamcast. Many, many hours playing 2-player and getting As on the missions while raising Chao with my next door neighbor as a kid. I don't think I realized how big my soft spot for this game was until I was playing through Sonic Generations(a great but but not one of my favorite games ever by any stretch) recently and it started bringing memories back. It has its flaws -- shoddy camera, terrible plot/VAs, occasionally frustrating gameplay, pacing issues relative to 2D sonic -- but I loved it, anyway.
Final Fantasy X
I'd have a hard time arguing that this was the best RPG in the series, but it's my favorite. The voice acting hasn't aged well, Wakka is one of the worst characters ever created who's basically an embodiment of everything I hate most in real life, Auron is an overdone stereotypical archetype, Tidus is kind of whiny, but you know what? I love the game anyway. I love the sappy plot with Tidus and Yuna, even though it led to the worst scene in RPG history(the laughing scene). I love Tidus even though he's pretty much a gigantic pussy for the first half of the game. There's some writing decisions that really sell the game for me, specifically the retrospective narration by Tidus, which I think adds a lot of maturity the story would otherwise have been lacking and develops his character some. Even though it was basically completely obvious I somehow didn't see the twist about Yuna Tidus finds out at Home coming, which made it one of the heavier scenes I can remember in an RPG. There's some other really swell scenes like the fights with Seymour, learning Anima, and the assault on the wedding that stand out in my mind. I loved the control of the summons as well, as long time fan of the series I'd always kind of wanted to play as Bahamut so I was pretty pumped to get to do that.
Dragon Age
It's nice of BioWare to save me from the disaster that is modern Square. There's a lot of characters that are kind of the roles you expect them to be... the snarky dark mage, the carefree rogue, that sort of thing, but there's a ton of depth on all of the characters that make them stand apart from the cast of other RPGs. For instance, Morrigan's ferocity is almost unmatched, and the cunning/cutting wit she provides is what you'd expect to go with it, but she has a softer, more vulnerable side the PC sees if they raise her affection a bit that makes her seem a lot more human than most RPG characters tend to be. Alistar, Zevran, and Lelianna are similarly well developed throughout the course of the game, which made playing through a treat... it's rare to have that many characters that come off as a passable humans in one game. The roleplaying elements of the game are some of the best I've seen in an RPG video game (typically you have 3-6 responses to prompts in dialogue that often lead to wildly different results and conversation branches) which made the game one of the most immersive I've played.
Mass Effect 2
I could probably just write the Mass Effect series here, though I think 2 is the most polished entry(at least until they fix 3's ending, which was otherwise a vastly superior game). It has many of the same properties that made fellow BioWare entry Dragon Age great, such as deep, believable character, but there's some things that ME just did a little better than DA did. The PC, Commander Shepard, being a character in his own right helped things a long a lot as s/he winds up being one of the funniest/most "bad ass" characters I can recall ever seeing in a video game. While Mass Effect 1's writing is better as far as the game's main narrative, I really appreciated the gameplay around ME2's ending mission, which I think is still pretty unique among video games. Unlike the rest of the series, party members can die at the end, and whether or not you lose squadmates is directly influenced by the preparations you made in the game up to that point and the decisions you make in the ending. Really makes the ending feel hectic and tense and real, like you have something on the line beyond just trying not to get game over screens, since it is one case where just plugging away through continues isn't enough to get the ideal ending.
Heavy Rain
This one is as much movie as game, but the whole "interactive movie" thing really worked for me. I bought my PS3 largely for the title and wasn't disappointed. Much like what I liked about ME2's ending, the possibility of character deaths kept me engaged(though unlike ME2, HR has no continues at all and all deaths are permanent), and the plot was compelling and well written. I appreciated that the identity of the killer was reasonably predictable based on the evidence in the game but hidden well enough that I didn't really have it figured out when they hit me with it. I found Ethan to be really relatable and tragic, which made it easy to push through the game. The psychological part of the game in the 3rd-5th trials was really interesting, since by then the game has you enough that you're not just doing shit to do it and are actually thinking about the consequences of what you're doing in a fictional world as though it was a real one. Heavy Rain did some things I don't think I've seen another game pull off.
Honorable mentions I'm too lazy to write about: Red Dead Redemption, League of Legends, Pokemon XD, FF4 and 6, Fable 1, NHL Series, MGS4, LoZ:LTTP, Pre-TBC World of Warcraft
Chrono Trigger
I believe this was the first game I played that I would still consider a great game. There's a few I loved when I first played them that don't appeal to me anymore as an adult, but I still think Chrono Trigger is one of the best RPGs on my time(a genre this list will have an obvious bias toward). It's not the RPG with the most depth or the best mechanics but it has more charm than almost any other game I've ever played. The story is compelling in spite of its simplicty, the characters are likable, and all the little things in the game are done well to keep you immersed and interested. Great soundtrack, too. The best of a great generation of RPGs, though it aged a lot better than most of its generational siblings.
Dragon Warrior Monsters
I'm not necessarily disappointed in the way history played out and the fact I wound up an administrator at a Pokemon forum or anything, but Pokemon games, while addictive, innovative, and amazing at creating communities and connecting people(which led to its success relative to competitors) were pretty much the worst monster games made.
Dragon Warrior Monsters was the most obvious spin-off monster game attempting to bite at that, given its release date, but it had some unique gameplay options that made it the best of its subgenre. The breeding system in this game was fantastic, leading to a tangible reward from breeding several generations of monsters to get the rarest, most powerful breeds of monsters(not to mention getting the best moves on them) that the ridiculousness of breeding in Pokemon with its hidden IVs and static species couldn't hope to match. The gameplay was simple and repetitive given the massive amount of randomly generated maps in the game, but the process of breeding massive trees of monsters to end up with the good stuff almost singlehandedly made this game the best of the series. There was some fun in hunting monsters down and trying to lure them with meat and the general exploration element(as well as being able to poach monsters from other breeders met in the wild), and some of the games bosses actually provided a reasonable challenge, something Pokemon and Digimon never matched very well.
Busy, busy, busy...
Monster Rancher 2
Like DWM, a game I''ve probably spent 400 or 500 hours with over the years. I actually bought my Playstation for this game as a kid because my neighbor was too much of a wimp to take his MR2 disc out and replace it with a different CD to get info to generate his monsters(which is the monster generation technique of the game) because he was worried it'd ruin his PSX or something, so I bought my own to prove the point. I haven't changed much over the years, I guess.
If I hadn't bought any PSX games after MR2 I think it would have been worth the money. I think this probably gets the title for my favorite game ever. Unlike the other monster games, which were RPG focused, MR2 is a monster raising simulator/strategy game where you tend to only have indirect control of the results(outside of battle, which has an auto mode I wouldn't suggest). Breeding monsters is pretty interesting in a way unique to MR, since monsters have a main breed and a subbreed (like Mocchi/Mocchi is a pure breed, but it could be part Suezo, which would be Mocchi/Suezo, which would make it look like a Mocchi in shape with Suezo-like-traits), and each subbreed would influence the resource regeneration, lifespan, and stats of the monster in question(the breeding system more or less works accurately as far as how alleles work IRL). The amount of variables that influences how strong your monster eventually got like managing tiredness, stress, hunger, training, exploration, and tournaments and the effects they have on the monster's lifespan was really engaging and combat tended to be reasonably challenging if you weren't horrifically overleveled for the class you were in. The Big 4 and the challenge events at the end of the game were surprisingly difficult and made me really work to beat the game as a kid. There's actually still a few monsters I've never had the chance to raise in spite of all the time I've spent with it, which I think says a lot for the game's depth. I can beat the game on one monster now after playing it so much over the years, but still usually do so once every summer or so because it's still amazing after so long. It's too bad this series didn't get more popular in the US, I think a lot of people would have really enjoyed it. Later entries in the series fell off a lot, but the two GBA titles were both excellent(especially the 2nd).
Boasts the most hilarious translation of any game I've ever seen. It's not like, Zero Wing, or whatever, but it's hilariously charming, especially later in the game when you can tell the translators pretty much just gave up. Some of the things the characters say throughout the game are just hilariously ridiculous. The best scene is definitely a really rare one that involves aliens landing, which unlocks Metalner for the player, which is just completely illogically written. I was playing it one summer at Psycho's apartment with his GF at the time and one of our other friends around and we were reading the dialogue of the game like a play for comedic effect and we pretty much completely lost it during that section because of how little sense it made. Lots of "..wait, what?"s.
Digimon World 1
I'm not quite as passionate about this one as the previous two monster games, and this one might not even objectively be better than Pokemon, but I liked it a lot more than any of the individual Pokemon games, anyway. Early in the game, balancing training with exploration and getting the right digivolutions(or in the case of most Ultimates, getting any digivolutions at all) was challenging and fun, and not having direct control of combat kept the game challenging even when it really shouldn't have been. The difficulty of raising a powerful monster nosedives as you get more resources(having enough gold to always use training boosting foods and the training manual is gamebreaking before you even factor in that you can basically get infinite chips by abusing some bad game mechanics and glitches), but the game remains charming enough that it's fun to finish, mostly. Horribly mistranslated, but in a lazy way rather than a funny way.
Pokemon Snap
The most fun game in the franchise. Sure, it didn't test my strategic mind or my reflexes or whatever but it was charming and the sticker station thing at Blockbuster was awesome. Bought this again for my virtual console a month or so ago and it was totally worth it. Has a special place in my heart for being one of the first games I remember completing 100% without any help from the internet or a strategy guide.
Metal Gear Solid
I don't think I really understood what storytelling in videogames was going to be capable of until this game. I actually really hate the gameplay in this series -- while I would objectively call the gameplay good, it just doesn't fit my tastes in genre -- but I suffer through it because the storytelling is amazing. It's one series where I'd really just be happier if it was a movie or a TV show or something, but it isn't, and it's been worth my money every time. MGS1 was one of the first games with full voice acting and it made an excellent script seem far more alive than any other game I'd played to that point. The soundtrack added a lot to it, and it just felt dramatic and terrifying in a way I hadn't seen in a game before. Snake, Naomi, Campbell, and Meryl are pretty fantastic characters that it became easy to care about. The humor is probably the high point of the game, as well as the series... stuff like Psycho Mantis reading your memory card (and that boss fight in general, which is my favorite in any video game ever) makes MGS stand out.
Final Fantasy Tactics
There was a time when this was as or more popular with the group that eventually created this site than Pokemon itself. I dare say if there was multiplayer FFT there wouldn't be a website for me to be writing this on myself. I kinda picked it up from them, and am glad I did. Another horrifically translated game (wait, where's Dycedarg's Elder Brother?), but it the difficulty was pretty challenging the first playthrough(as long as you don't use Orlandu!) and SCCs and such kept it fun on repeats. Surprisingly good plot with the war of the lions and the backstabbing and all of that noise. Some great characters in Delita, Zalbag, Wiegraf, Agrias, etc. Another one of those games I can play through basically an infinite amount of times.
Chrono Cross
I really hated this game the first time I played through it because it wasn't the sequel I wanted for Chrono Trigger, but I warmed up to it over time. It's a fantastic game in its own right, with one of the most complex plots an RPG has ever seen(though it presents it ambiguously enough that it's almost impossible to piece together without outside help... there's a FAQ about it on GameFAQs that I think is nearly as long as the game script). There's a few too many characters, but the alternate dimensions thing allowed for some neat writing opportunities showing different ways characters' fates could have changed as well as some major ones with that region of the world itself. Some really fantastic characters in Harle and Kid, which make me wish the game had focused more on developing fewer characters given how well they did with what they bothered to develop. Some of the more emotional RPG moments with the flashback to the burning orphanage and the fight with Miguel set the game over the top. Also has my favorite video game soundtrack of all time.
Sonic Adventure 2
OK, I'm really straining my credibility with this one but since this was "favorite" rather than "best" I feel good listing this. I totally hear people who complain that Sonic was always way better in 2D, but I only had a SNES in that era of gaming and I had a fantastic time with Sonic on the Dreamcast. Many, many hours playing 2-player and getting As on the missions while raising Chao with my next door neighbor as a kid. I don't think I realized how big my soft spot for this game was until I was playing through Sonic Generations(a great but but not one of my favorite games ever by any stretch) recently and it started bringing memories back. It has its flaws -- shoddy camera, terrible plot/VAs, occasionally frustrating gameplay, pacing issues relative to 2D sonic -- but I loved it, anyway.
Final Fantasy X
I'd have a hard time arguing that this was the best RPG in the series, but it's my favorite. The voice acting hasn't aged well, Wakka is one of the worst characters ever created who's basically an embodiment of everything I hate most in real life, Auron is an overdone stereotypical archetype, Tidus is kind of whiny, but you know what? I love the game anyway. I love the sappy plot with Tidus and Yuna, even though it led to the worst scene in RPG history(the laughing scene). I love Tidus even though he's pretty much a gigantic pussy for the first half of the game. There's some writing decisions that really sell the game for me, specifically the retrospective narration by Tidus, which I think adds a lot of maturity the story would otherwise have been lacking and develops his character some. Even though it was basically completely obvious I somehow didn't see the twist about Yuna Tidus finds out at Home coming, which made it one of the heavier scenes I can remember in an RPG. There's some other really swell scenes like the fights with Seymour, learning Anima, and the assault on the wedding that stand out in my mind. I loved the control of the summons as well, as long time fan of the series I'd always kind of wanted to play as Bahamut so I was pretty pumped to get to do that.
Dragon Age
It's nice of BioWare to save me from the disaster that is modern Square. There's a lot of characters that are kind of the roles you expect them to be... the snarky dark mage, the carefree rogue, that sort of thing, but there's a ton of depth on all of the characters that make them stand apart from the cast of other RPGs. For instance, Morrigan's ferocity is almost unmatched, and the cunning/cutting wit she provides is what you'd expect to go with it, but she has a softer, more vulnerable side the PC sees if they raise her affection a bit that makes her seem a lot more human than most RPG characters tend to be. Alistar, Zevran, and Lelianna are similarly well developed throughout the course of the game, which made playing through a treat... it's rare to have that many characters that come off as a passable humans in one game. The roleplaying elements of the game are some of the best I've seen in an RPG video game (typically you have 3-6 responses to prompts in dialogue that often lead to wildly different results and conversation branches) which made the game one of the most immersive I've played.
Mass Effect 2
I could probably just write the Mass Effect series here, though I think 2 is the most polished entry(at least until they fix 3's ending, which was otherwise a vastly superior game). It has many of the same properties that made fellow BioWare entry Dragon Age great, such as deep, believable character, but there's some things that ME just did a little better than DA did. The PC, Commander Shepard, being a character in his own right helped things a long a lot as s/he winds up being one of the funniest/most "bad ass" characters I can recall ever seeing in a video game. While Mass Effect 1's writing is better as far as the game's main narrative, I really appreciated the gameplay around ME2's ending mission, which I think is still pretty unique among video games. Unlike the rest of the series, party members can die at the end, and whether or not you lose squadmates is directly influenced by the preparations you made in the game up to that point and the decisions you make in the ending. Really makes the ending feel hectic and tense and real, like you have something on the line beyond just trying not to get game over screens, since it is one case where just plugging away through continues isn't enough to get the ideal ending.
Heavy Rain
This one is as much movie as game, but the whole "interactive movie" thing really worked for me. I bought my PS3 largely for the title and wasn't disappointed. Much like what I liked about ME2's ending, the possibility of character deaths kept me engaged(though unlike ME2, HR has no continues at all and all deaths are permanent), and the plot was compelling and well written. I appreciated that the identity of the killer was reasonably predictable based on the evidence in the game but hidden well enough that I didn't really have it figured out when they hit me with it. I found Ethan to be really relatable and tragic, which made it easy to push through the game. The psychological part of the game in the 3rd-5th trials was really interesting, since by then the game has you enough that you're not just doing shit to do it and are actually thinking about the consequences of what you're doing in a fictional world as though it was a real one. Heavy Rain did some things I don't think I've seen another game pull off.
Honorable mentions I'm too lazy to write about: Red Dead Redemption, League of Legends, Pokemon XD, FF4 and 6, Fable 1, NHL Series, MGS4, LoZ:LTTP, Pre-TBC World of Warcraft