I myself, like story-driver first-person shooters (Half-life), real time strategies, a big fan of RPGs (Morrowind, Oblivion), and old classics (Super Mario). Well, I don't really consider myself limited to any selection of genres, since I would play anything that is fun and can keep my attention.
World of Warcraft was fun while it lasted, but I didn't want to keep paying the subscription when I was too busy to play.
When I shop around I tend to go for games with high replayability or large enough to keep me amused for months - so I go for epic RPGs like Oblivion, open-ended strategy games like Civilisation and Spore. Nothing would be worse than spending $70-$100 for a game which you complete in 3 hours

I also like Xbox Live Arcade games like Rez HD, 3D Ultra Minigolf Adventures, Band of Bugz and just browsing around the Live Marketplace to see what I can find

I'm mostly an Xbox 360 gamer although I use to (and still do occasionally) play PC games.