I like pretty much all genres, though FPS are by far my favourite. I think I like that genre more because it is a direct test of skill where you have complete control of the players motions and actions. Which can be both a good and bad thing, as in
Republic Commando where it took me a few ... unpleasant and bloody demises ... to get used of throwing grenades with the left-hand. It's just embarrassing when you grenade yourself.
If you judge what one's favourite game is based on how much time one spends playing it, I guess that would have to be
Modern Warfare 2 as Steam is counting at least 80 hours - too much time playing the special ops missions.
Unfortunately I only play offline. I tried playing
Battlefield 2142 online back in the day, but with pings of around 300 plus I was struggling to keep a 1:1.5 kill/death ratio. When I got killed by the same player three times in three different engagements without landing a shot, well, I can take a hint.
He probably would have killed me anyway, but he had already moved on the server by the time I had fired straight at him on my computer.
But I do love the other genres (in order of most enjoyed genre):
Simulations -
Star Wars X-Wing Alliance - it would
TIE Fighter, but those advanced concussion missiles kind of takes enjoyment out of dogfights.
RPG -
Mass Effect.
RTS -
Star Wars Empire At War.
Racing -
NFS Hot Pursuit.