For me, it has to be FPS. There has hardly been one over the years that I didn't find enjoyable in some way or another, and most of them are fun as all hell. I even found Operation:Bodycount to be entertaining for christ sake, and anyone who played it for more than 10 seconds at a go knows just how crappy that one was. Anyway, I'm curious to know what other people like to play more than any other game type. Be it FPS, Adventure, RPG or puzzle games.

cRPGs & TBS. Slower & focuses on thinking/planning rather twitch.
I'll play FPS games now & then, but I don't have the reflexes to keep up with most people.
Lately though, I've been drawn to Tower Defence style games. Normally I would not even bother, but there is something too these things that gets me.

Strategic RPGs, also turn based strategy.

Starting from fave to less fave:
1. RTS
2. FPS/TPS
3. TBS
4. MMORPG
5. RPG
6. Board games

RPG. Specifically, open-ended RPGs with focus on exploration and loads of stuff to discover "off the main road". Too bad there are few such games.

1. RPG
2. TBS (Both grand scale and tactical)
3. Space Sims
4. Economic Sims

FP-RPG
I must admit that i do enjoy FPS games. There is something about them that makes them more immersive than most other genres.. i feel more like i'm in the world, rather than feeling like i'm playing a game.
I also like that they tend to be easy to drop in or out of for a short time (unlike games like RTS where you often have to do a whole level for an hour or so). And they don't tend to be too long, so they don't usually have time to lose momentum or get boring.
That said, my favorite FPS games are the ones that included some RPG elements (but not too many). Deus Ex, System Shock 2, Jedi Knight (1, not 2).

fav: in order more or less
RPGs.
FP Shooters
Strategies
least favorite
racing games
realistic simulators

Turn-Based RPG's are my hands down favourite(Good example is the Final Fantasy series).
I also really like RTS games(Such as the Seven Kingdoms series) and Adventure games(The Myst series).
FPS(Like Bioshock) and TPS(Like the Metal Gear Solid series) are pretty good as well.

It is very hard for me to say, because there really isn't a genre that I have always liked above the rest. There are games I like more than others, but not genres. I often find myself in moods for one genre or another but there is no stand alone favorite.

1. FPS
2. RPG/RTS
3. Space Simulators
4. TPS
5. Platformers/adventure games/jRPG(only tried 3-4 jRPG's, so can't say much about them)
Which is probably all that I play. I might play some random board/card game from time to time, or even the odd Magic: The Gathering, but not much beyond that.

1. RTS
2. Racing
3. RPG (including MMOs)
4. FPS
I really like just about any game though, I especially enjoy playing adventure games, such as Sam and Max or the old Indiana Jones games.

If I have to pick just ONE I would have to say sand box games (preferable but not exclusive to third person perspective).

Guess I'm going completely against the flow here :)
1. Adventure
2. RPG
3. Casual

1. Western RPGs, JRPGs like the Final Fantasy series just bore me these days
2. FPS games, but not FPS RPGs, weird, huh?
3. Third person action games