Talking with a friend today made me think about this a little.
Some people are very dedicated to a genre of gaming. Everyone knows someone who's got every Madden ever released, or who salivates for Square-Enix. Me... I'm not like that.
I've played and enjoyed some shooters, RPGs, puzzle games, old-school adventure games, new adventure games, MMOs, PS3 games, stealth games, board / card game adaptations, PC games, DS games... I've enjoyed "girly" games (a description for another time) and explosively violent games. I like God of War and Metal Gear Solid and Phoenix Wright and Monkey Island and a whole bunch of other titles and franchises.
Honestly, from my admittedly brief (~ 8 months) run as a GameStop employee, and my not-so-brief (~ 20-year) history as a gamer, I think it's useful to see the whole range. No-one's going to enjoy playing everything; I certainly don't. But it's brilliant to see genres kind of cross-pollinate. A game like Fallout 3 draws from the RPG, the FPS, and even at times the old adventure game. And then there are the more indie / avant-garde titles available as downloadable short-form games: Flower, World of Goo, and Braid among them. Those games tend to meld, reinvent, or avoid genre entirely.
I never thought anyone would see me playing a survival horror game, and then I turned out to kick ass at Resident Evil 4 when my ex-boyfriend left the controller unguarded for a while. There wasn't a Japanese RPG on Earth that could captivate me, but then Chrono Trigger and The World Ends with You (both on DS) managed to grab me in for at least 50 hours each.
So I doubt I'll ever enjoy a Final Fantasy game... but once upon a time, I'd never enjoy an FPS, either... and then there was BioShock. Never say never.