Action adventure: God of War III.
FPS: Bioshock.
RPG: The Elder Scrolls IV: Oblivion. (Haven't played Skyrim, yet).
Platformer: LittleBigPlanet.
Racing sim: Forza Motorsport 4.
Racing arcade: PGR4.
Vehicle Combat: Twisted Metal: Black.
TPS: Gears of War 3.
Puzzle: Tetris.
Fighting: Mortal Kombat.
There's my list, with a few added categories :)