Shockingly I would have to say Strategy. I just love being like a commander of a army, or the Duke/King of a kingdom. Sending people to do my... well, stuff. And some games you are a soldier (so you get to fight) but you're also leading a troop. So strategy hands down.
The only type of video/flash game I don't like, with the exception of racing, is sports. They don't usually play all that well and even if they are decent games, I'd rather play it in real life.
I like strategy too. Games like Warfare 1917 or Age of War are cool. I do like the "Puzzle & Skills" section too! "I Love Traffic" is such a good game.
I like "Puzzle and Skill." I used to be pretty srictly that section... but no longer. I guess it depends on the game, but I think "Adventure" is next on the list.