<3 musical rhythm games ... durned Guitar Hero and Rock Band. (Though it did get me to pick up the real thing, so there's some good to 'em :P)
RPGs, well, yeah, easy pick; your Final Fantasy, your Seiken Densestu, your Elder Scrolls and Fallout, I lurves them. Engrossing storyline and actual character development, yay! Sandbox play with little to no characterization in the protagonist, sure! As long as it's fun, I'd play as a plank of wood against an army of chainsaw-wielding aquatic dam-building rodents~
Puzzles and platformers, the "chocolate" and "peanut butter" of video gaming - mix 'em in any other genre, and I'm all over it. Mix 'em together, and you'll not see me til the danged thing is solved.