I am a sucker for both puzzle games and RPGs, so Dungeon Raid is right up my alley. It's a puzzle game where you have to match up various icons on a grid, as you can see above, but the real draw here is that all of those icons map to various RPG abilities that then let you level and grind out a sword-and-sorcery style character. Matching up swords and skulls, for example, lets you attack monsters, while matching coins piles up gold to spend on items later on. Leveling up grants various abilities and spells that affect combat, and as you play the puzzle game, you're also building up a character and casting spells at the same time.
It's a great mix of the two genres, done in a pretty original way, and the game moves quickly enough that it's easy to summon up that "just one more turn" feeling as you play along. The game's polished and runs great, full Game Center and OpenFeint integration provides leaderboards, and there are four difficulty levels to play with and lots of random items to pick up as you play. Dungeon Raid is currently US$2.99 on the App Store.