This is such a great question, and I really can't think of any single genre that would be my favorite. It all depends on the mood I'm in, but that can change from day to day (or hour to hour). Here's a few that I definitely like, though:
Puzzle, Epic Quest (Metroid Prime 3, Legend of Zelda: PH/TP, God of War, etc)
Platformers (Super Mario Bros - Super Mario Galaxy, Megaman 2, Contra 4, etc)
Fighting (Tekken Tag, Smash Bros, etc)
Arcade -as in, non-realistic- Racing (Excite Truck, Mario Kart, etc)
RTS (Starcraft 2 needs to come out before I murder someone)
And, to be honest, many more but I've already listed 5 (in random order, and possibly not even top 5), so I'll stop.
No wonder I can't even keep up with games coming out that I want to play!
Puzzle, Epic Quest (Metroid Prime 3, Legend of Zelda: PH/TP, God of War, etc)
Platformers (Super Mario Bros - Super Mario Galaxy, Megaman 2, Contra 4, etc)
Fighting (Tekken Tag, Smash Bros, etc)
Arcade -as in, non-realistic- Racing (Excite Truck, Mario Kart, etc)
RTS (Starcraft 2 needs to come out before I murder someone)
And, to be honest, many more but I've already listed 5 (in random order, and possibly not even top 5), so I'll stop.
No wonder I can't even keep up with games coming out that I want to play!