Platformer: Super Mario 64 DS
RPG: Final Fantasy IV Advance
FPS: Halo 2
Strategy: Final Fantasy Tactics Advance
Fighting: Soul Calibur II
Beat 'Em Up: Super Smash Bros. Melee
Sports: Mario Power Tennis
Action/Adventure: The Lord of the Rings: Return of the King
MMORPG: RuneScape (mainly because this is the only MMO I have played)
Puzzle: Pokémon Puzzle League
Racing: Mario Kart DS