Mine are...

Action Adventure: Onimusha I(PS2)
RPG: Final Fantasy VII(PS)
Racing: Mario Kart(GC)
Fighting: Mortal Kombat(SNES)
Sport: WWE Smackdown Vs. Raw 2006(PS2)
FPS: Duke 3D(PC)
Platformer: Crash Bandicoot(PS)
Puzzle: Tetris(NES)
Puzzle Adventure: Broken Sword I(PS)

And if you can think of any more genre's, please add to the list.