Footnotes of the new additions for your consideration (ignoring Megas for now, as well as Fairy teams, as they deserve their own post). One thing of interest this Gen is that with a few exceptions, most of the mons introduced this Gen are useful is some way and have well defined niches. Very few deadweight mons.
Bug
Vivillon - Potent Quiver Dancer, but faces stiff (overwhelming, even) competition from Volcarona, Venomoth, and Yanmega for a spot on the team.
Dark
Greninja - Wait, this thing's a Dark type? With it's Protean ability allowing it to become any type of its choosing, Greninja becomes an extremely versatile addition to Mono-Dark teams.
Malamar - Great coverage and boosting options between its STABs and Contrary Superpower, meh base stats and defensive typing will likely hold it back from becoming a mainstay.
Pangoro - Meeeeeh. Movepool is a huge letdown despite the interesting Parting Shot. Scrafty does Fighting/Dark better.
Dragon
Dragalge - Solid Special wall, solid power thanks to Adaptability, and its Poison typing makes it a Dragon teams best answer to Fairies.
Goodra - Huge Special wall, finally putting mono-Dragons resistances to good use, alongside several great abilities, great movepool, and decent mixed attacking stats
Noivern - The fastest Dragon type available and a potent Specs user, will face considerable competition from Lati@s
Tyrantrum - Capable Dragon Dancer with two solid abilities and the movepool to abuse them.
Zygarde - Versatile sweeper with great bulk. It and to a lesser extent Tyrantrum fill the large physically-defensive void Dragon teams previously had.
Electric
Dedenne - No.
Heliolisk - On a mono-Electric team, Heliolisk is rather meh, and faces competition with a plethora of other speedy Special Attackers. Bringing 2 immunities to the traditionally frail type will be its main niche.
Fighting
Chesnaught - Solid physical bulk and a great support movepool (a luxury among Fighting-types).
Hawlucha - Fastest non-Mega Fighting-type available, with great offensive typing. Potent Band user.
Pangoro - Still meh.
Fire
Delphox - Good Special Attacker/Sweeper, but nothing terribly special.
Pyroar - Actually, scratch that. THIS is nothing special, at least for a Fire type. Good SpA and Speed, but terrible abilities and movepool.
Talonflame - One of the defining forces of Gen 6, SD and extremely powerful priority make for a terrifying addition.
Flying
Hawlucha - Speed is less impressive amongst Flying types, but still a solid Band user.
Noivern - Again, Speed is less impressive here, but still a solid Specs user.
Talonflame - Yep, still terrifying.
Vivillon - Less Quiver Dancing competition, but still competes with Yanmega. Luckily, there aren't many other Flying-type Special sweepers.
Ghost
Aegislash - Incredibly unique tank with great defensive typing. Overhyped maybe, but still a major addition.
Gourgeist - Now in 4 different flavors! Although only 2 really matter. Take either the physical tank, or the less bulky but speedy supporter.
Trevenant - Man this is probably my favorite mon. Its stalling ability between Leech Seed and Harvest is hilarious.
Grass
Chesnaught - Support movepool is less impressive for a grass-type, but still effective and has unique access to Spiky Shield.
Gogoat - Criminally overlooked, Gogoat is easily the most perfectly designed Bulk Up user ever, owing to great special bulk, good attack, Leech Seed, and Horn Leech.
Gourgeist - Man Gourgeist, your functional but kind of boring.
Trevenant - Still stalling away.
Ground
Diggersby - Even this Gen's derp rodent is good, thanks to Huge Power and priority.
Zygarde - Take Hippowdon, remove Sand Stream, add more Special bulk, versatile sweeping capabilities, priority, and dragon.
Ice
Aurorus - Ice-teams now have two Hail-inducers with terrible defensive typing! Aurorus at least has serviceable bulk, but its offensive abilities aren't as impressive as Abomasnow's.
Avalugg - The physical wall for Ice teams, and a decent spinner to boot.
Normal
Diggersby - Huge Power, and a STAB that wrecks the Rock and Steel types that wall Normal.
Furfrou - Can take physical hits like a champ, but is unimpressive beyond that.
Heliolisk - Stands out more here than on Electric teams, as most special attacking Normals lack Heliolisk's speed, and its Electric STAB hits all Normal resists neutrally.
Pyroar - Once again stands out more here for the same reasons as Heliolisk. In addition, its Fire STAB allows it to roast Steels.
Poison
Dragalge - Not as crucial to Poison as it is to Dragon, but still a potent Special tank.
Psychic
Delphox - Underwhelming here due to the plethora of Special sweeping Psychics, although Fire STAB allows it to beat Steels.
Malamar - Physical attackers (and physical attackers with good coverage) are less common among Psychics, so Malamar stands out a bit more here than on Dark teams.
Meowstic - Prankster's cool, but lacks good moves to abuse it with, and it a mediocre sweeper for a Psychic type.
Rock
Aurorus - Only reason to use this is Snow Warning, which no good on a Rock team.
Barbaracle - Powerful physical Shell Smasher, and... yeah.
Carbink - Great mixed bulk held back by lack of offensive presence or support movepool.
Tyrantrum - Solid physical sweeper with unique coverage for a Rock-type.
Steel
Aegislash - It's Aegislash. Am I done yet?
Klefki - Great defensive typing and effective Prankster movepool.
Water
Barbaracle - Again, not much to say. It's good at what does, although must now compete with Cloyster.
Clawitzer - Man, such a cool, wasted design. Great Special Attack and movepool, but mediocre bulk, poor Speed, and lack of boosting options prevent it from putting it to good use.
Greninja - Still here, breaking all the monotype rules.