I love games which are not too complex for me to learn how to play it. Even simple first person shooters can become quite complex for me as I cannot remember shortcuts on the keyboard, or forget which mousebutton to use.
But I do like fps games, adventure games, browsergames (depending on which they are)
Man, this is kind of a hard choice. I play a lot of games. I'm gonna have to say Real Time Strategy games are the ones I like to play the most. Oh yeah and I forgot about Minecraft, that's a fun one to do. Love the sandbox-style stuff too.