Third Person shooters/TPS/3PS (Ratchet and Clank)
first person Shooters/FPS (Halo)
RPG's/JRPGS's (Final fantasy)
Platformers (Mario, Klanoa)
beat 'em ups (Ninja Turtles)
Shoot 'em ups (Gradius, Ikaruga, Star Fox)
fighters (Street Fighter)
Puzzle (Tetris, Bejeweled)
Rhythm and music (Guitar Hero, Rhythm Heaven)
Board Game (....Monopoly?)
Exploration (Metroid, Shadow Complex, Tomb Raider)
Other Genres I might have missed