I recently (like two days ago) discovered King of Thieves on my app store. It's by ZeptoLabs, the same guys who created Cut The Rope; it has the same unique and consistent aesthetic and really polished/fluid/animated interfaces and gameplay. It took me a while to really get a feel for it, but basically it's a platformer with some unique controls and mechanics and you either run the single-player gauntlet of dungeons, or try other players' dungeons. The other player dungeons are where things shine, because you get to design your own dungeons from templates! The best part is, you cannot save what you cannot beat (twice in a row actually, although you can try as many times as you want).
This leads to all sorts of crazy experimentation where people try to find something that is solvable, but difficult enough to discourage other players. I have begun to really enjoy designing dungeons and then eagerly waiting for hordes of people to test it out for me, leaving piles of skulls and gold.
As is the norm, the game is freemium with free gameplay and paid items to help speed things up. The official web-site with info is at http://www.kingofthieves.com/