Survival horror, rpgs, action-adventure, anything action-related, It's ok to just shoot around but it is also nice to have a very well-thought-through games with a story and puzzles.
Other genres of games that interest me are Action and Story based Drama games. Some of my favorite games based on these genres are GTA V, GTA San Andreas, GTA Vice City, Hitman Absolution, Call of Duty :Black Ops.
I love the FPS genre - recently I've been playing BF3, BF4 (Beta), Borderlands 2 (Play it with your friends - it isn't that fun alone), FireFall and Payday 2 (Again, play this one with your friends, really recommended). I also love sandboxes, such as GMod.
Fighting games, FPS and open world. These 3 are pretty much the only genres I like. I don't mind platformers and sports game as such, just don't play them a lot.
My favorite genres would be Role Playing, Action, Adventure, FPS, and Strategy! I'm a die hard steam gamer and enjoy a lot of genres. Lately my friend has bought me crusader kings 2 which really pulled me into the strategy genre. Hopefully with the more games I play, I will start to enjoy even more genres!
I absolutely love the FPS genre. I've been playing FPS games for as long as I can remember and I'm not stopping any time soon. I love games such as Battlefield, Call of Duty, Halo, you name it.
I like fighting games equally to racing games. I'm equally average on both genres though, and my friends could probably beat me on either on an average day. Still very fun for me though even if I keep losing.
Big RPG fan - Final Fantasy, the 'Tales of' series, and Pokemon in particular - but I've also gotten into Awesomenauts recently; it's a 2D platformer-styled MOBA, similar vein to Dota and LoL. Much more accessible, which is nice (I tried Dota a few times and just couldn't get the hang of it).
I really like sims and "tycoon" games. Don't seem to be too many out there that interest me at the moment. I like the look of Prison Architect but it's very expensive for an alpha.
The other genres that I play a lot of games of are FPS and Third Person Action Adventures. I also play some RTS games and RPG's. Essentially, I play almost anything except Puzzle games.
I also like RPG's, shooters, flying simulators, strategies and soccer games. For example now I play a fantastic survival action adventure game called The last of us, 3 shooters Swat 3, BF4 and COD: Ghosts and the new FIFA 2014 soccer simulator.
I enjoy Action and Adventure games of course, as well as Sports games. However on genre that I enjoy a lot is Horror games such as Zombie games. I don't why but they are always entertaining to me.
I love RPG's and MMORPG's, I like the leveling, upgrading and the feeling of progressing my character.
In racing games I also love this feeling when you have games that you can upgrade your cars like Need for Speed Underground for example.