Any game where you can create and share your own levels is alright in my book. A level-sharing community allows different minds to challenge others in original ways, therefore allows endless possibilities.
TD games that involve the user as much as possible. RPG's because... well, they're RPG's and they interest me. FPS... because its addicting. And of course Adventure and Arcade.
I hate Puzzle games with a passion. Rarely do I ever enjoy those kinds of games. Action is okay I guess, but Strategy (Tower Defense especially) is my favorite.
I am pretty much versatile when playing games. I like shooters, actions, puzzles, strategic, and arcade games! I am a gamer who likes everything. But I hate full blown medieval adventure games. They're so corny and hard to understand. Truly just hate them.