First and foremost would be a War Mace/Willpower scrapper. I've been playing the game since I was about 7 years old and I never really learned how to play anything other than "run in and hit numbers at it until it's dead". I heard from a frequent collaborator that Willpower can be slotted in such a way that makes your character damn near unhittable. I haven't double checked this idea (I've been informed that I have a terminal case of "filthy casual") but I've been meaning to give it a shot, for kicks. (literally.) Being an elusive, terrifying ninja with a silly cartoon hammer just seems like the perfect blend of really cool and really stupid. Right up my alley.
Second up would be a strong Defender. I've never rolled up any kind of support character (except one half-assed Mastermind on Redside that I might have to abandon), and I've always liked playing the healer/buffing boy in other games. (If it's anything like playing the Medic in TF2, then I'm interested.) I mostly want to be that guy that lets everyone have effectively infinite endurance, because whenever I'm playing a melee character on a team with a defender that can do that, I'm having a hell of a lot of fun. World needs more supports anyways.
Third would be anything with a Mutation origin. I don't really build characters around their powers, I just like to make characters in my head and give them whatever powers seem to fit. I want to try to run up a Blueside mastermind with a Mutation origin of some kind, but I haven't really thought about it much further than that.
Reading through this thread is daunting, to be honest. You guys seem like you understand the game down to the metal.