I'll only include one game per franchise to stop it from being monotonous.
I'll put five in each so I don't have to feel bad about not including stuff.
Action:- No More Heroes 2: Desperate Struggle
- Shadow of the Colossus
- The Legend of Zelda: Twilight Princess
- Castlevania: Symphony of the Night
- Metal Gear Solid, haven't a clue which one specifically
(Not really sure what differentiates Action and Action-Adventure so I just stuck 'em all here. )Platform:- Oddworld: Abe's Exoddus
- Croc 2
- Bugs Bunny & Taz: Time Busters
- Kirby's Fun Pak
- Alice: Madness Returns
Fighter:- BlazBlue: Chrono Phantasma
- Persona 4 Arena Ultimax
- SoulCalibur II
- Guilty Gear X
- King of Fighters XIII
Puzzle:- Zero Escape: Virtue's Last Reward
- Danganronpa 2: Goodbye Despair
- Lumines: Electronic Symphony
- Phoenix Wright: Ace Attorney
- Beat the Beat: Rhythm Paradise
(I don't know if most of those are technically puzzle games but they don't have anywhere else to go on the list)Shoot 'em Up:- Panzer Dragoon Orta
- Touhou, in general
- Mars Matrix
- Triggerheart Exelica
- Ikaruga
JRPG:- Final Fantasy VIII
- Shin Megami Tensei: Persona 3 FES
- Lost Odyssey
- Digimon World 2003
- Tales of Graces f
WRPG:- The Elder Scrolls III: Morrowind
- Mass Effect 2
- Dragon's Dogma
- Fallout 3
- Fable: The Lost Chapters
Horror:- Silent Hill 2
- Project Zero
- Amnesia: The Dark Descent
- Alien: Isolation
- Eternal Darkness: Sanity's Requiem
Strategy: - Warcraft III
- Heroes of Might & Magic III
- Age of Empires II
Yeah, haven't really played many strategy games.
FPS:- BioShock
- Unreal Tournament III
- Alien Trilogy
- Darkwatch
- Doom