So many iconic moments to list, but one moment that really sticks out to me that I feel often gets overlooked involves the legendary Johto beasts and the first ever legendary Pokémon theme in the main series games.
In RBY and GS, all Pokémon shared the same typical wild Pokémon theme. But in Crystal, Raikou, Entei, and Suicune finally broke the mold with their own unique battle theme. Whether you're just randomly walking through grass in Johto and suddenly here a different and loud theme kick in, or finally engage Suicune in battle at the Tin Tower after chasing it across the region, the first true legendary Pokémon theme makes the encounters with the Johto beasts one of the more memorable moments in the series.
Your rival being the champion in RBY wasn't that surprising, but that doesn't make it any less iconic imo. He was always one step ahead of you throughout the whole game, but the champion battle is the moment when you finally caught up to him and ultimately surpassed him on an equal battlefield in one epic final battle.
I would say Lance being the Champion in GSC. After Red left, we see Blue became the Viridian Gym Leader... such a demotion. Why didn't Blue become the returning Champion? It's like a First Runner Up getting to the top spot when the grand prize first place winner cannot continue... but when First Runner Up cannot continue, leave it to Second Runner Up. Lance makes 3rd place look like First!
Lance, is iconic because he was the first "Cool" trainer. When I was a kid and looked at my older brother when he said "Lance looks like a Super Saiyan" on RED I immediately tried to look but he took it away and said "you have to make it to him yourself." I didn't even have the game at that point but when I finally got RED and I beat Agatha for the first time and got to him, having forgotten the moment my brother saw him for the first time, I read each line of the text slowly. Then... the battle sequence and theme started, and sliding across the screen I saw what I realized was not a false hope or lie, my brother was absolutely right!
A cape, a mountainous layered haircut with peaks and edges, and a Dragon "Master" (Trainer) just like DBZ features Dragons.
I faced Gyarados, which now that I think of it reminds me of the DBZ dragon with no wings, but can Fly, and the mustache and fins.
When you beat him, and realize Blue is your rival, you still think Lance is cooler. He has Dragonite, Gyarados, and even the cool Dragonair which is like a mini Gyarados more than a pre-evolved Dragonite. It's emotionless expression is priceless, simply indifferent and cool.
Then... GSC comes out, and you met a Claire, and realize she is related to Lance. You think, these 8 gyms all feature types that the Gen 1 didn't include. You know they wouldn't repeat types in the E4 (ironically as I write this I do realize I am wrong... but not about Claire+ Lance, but rather Bruno still using fighting types when they have a fighting gym-Chuck).
Then you reach the E4 and think, they replaced Lorelei, and Agatha, and Lance... and you still wonder why they would make the Dragon trainer connection with Clair and Lance... and laugh to yourself "lol, Claire uses Kingdra... why even include her, they should have used Dark instead because she seems too much like Lance"...
And then... you face your fate as you walk past Karen and see... Lance!
It feels surprisingly fitting. He is the best of the best, it almost surprises you that a Dragon Master could lose to 2 kids, so it seems even more appropriate that he is now the Champion... for now.
And finally, you get to face him, a Master! (at least of one type- even if it's really Flying rather than Dragon... I guess I was wrong because like Bruno and Chuck, he has the same type as Faulkner- But as a Champion, he technically isn't a member of the E4 so it's okay). He is the badass that watches you face Red Gyarados in the Lake of Rage, trusting you can capture it without his help, but being there just in case you need backup.
The battle in GSC here feels more iconic than in RBY because he ties the two regions together which makes it come full circle. He is the former E4 of Kanto, now Champion of Johto and is related to Claire, a Dragon gym Leader of Johto. It's like you beat the Champion of multiple regions... (lol the Johto league is actually still in Kanto, no wonder Koga didn't mind the promotion, no traveling off too far).
Previously, you faced him in Red, Blue, and Yellow which confirmed your heartfelt beliefs that Gyarados and Aerodactyl counted as Dragons, simply because Lance uses them. (He cannot use Charizard because your rival, Blue, is secretly next- and may have it if you picked Venusaur).
Next, as the final Champion in GSC, with no Red or Blue immediately afterwards who may have Charizard as starters, once you beat him, you feel like your heartfealt beliefs of Charizard counting as a Dragon is fully realized, again solely because Lance uses them.
Not to mention that the levels of his Pokémon are lower in GSC than RBY, which means not only did he catch new Pokémon that he had last Gen, but he raised and leveled them up from scratch... that's dedication man! Blue and Red kept their Pokémon in GSC from RBY, Lance is such a boss that he didn't mind getting new Pokémon and making them nearly as powerful as before, hence keeping his Championship title until you claim it!
This is why Lance's final battle with you is more iconic than Red in GSC, or Blue from RBY, Lance connects it all without breaking a sweat!
And... pfft... he doesn't bother with Kingdra like Claire, he would rather use 3 Dragonites... until the rematch in Fire Red and Leaf Green.
In fact, he is the first And only Champion to ever get this promotion from E4 to Champion. He, and he alone is iconic enough for this to be something only he can claim.
When you think of Claire, you think of Lance, when you think of (Red/Any) Gyarados, you think of Lance, Dragonite, etc. When you think of Cool, Champion, Badass... Lance.
He is literally what made the show's Lake of Rage arc awesome, he was the only member of the G-Man group. Lance doesn't disappoint, it feels more awesome to face him than Blue, Red, or anyone else really. Red has higher level Pokémon, but that includes a Pikachu :(
Speaking of final battles: here!
Lol, we know the Final battle isn't with Lance, but guess whose in the video thumbnail? Not Blue...
Also: Gen 1 V Gen 2