Titus is a game that calls itself a "political simulator," featuring an agoraphobic watchmaker who decides to run for president in the crazy world of Wealland. If that description and the game's Tim Burton-esque aesthetic haven't won you over already, then you and I have very different tastes in gaming.
The actual gameplay is more about how well you do at minigames than actual strategy, but it's a fun affair, providing a tweaked parody of politics and that really interesting art style. Titus' main opponent is a mime, and through minigames that have you catching cash or Doodle Jumping-your way along, it's your goal to win the hearts (or at least the wallets) of your people.
Titus has achievements, but unfortunately it isn't directly Game Center enabled. It is a universal app, however, and it's available right now for US$1.99.