Samurai Girl is a 2D Korean RPG on iOS that's surprisingly deep. The combat is pretty traditional 2D stuff, but this game has all of the features that you'd expect in a full RPG, including over 50 quests and various skills to earn, a full collectibles and crafting system and even a pet system, which the game claims is the first ever seen in an action RPG (I'll argue that Torchlight has pets, but whatever).
Unfortunately, the game suffers from a pretty cluttered UI, so while the controls are responsive, it might take a little getting used to all of the buttons and seeing around them. But the action is pretty fast and furious, and while the game's Korean heritage doesn't do it any favors (it can be a little confusing knowing where to go and what to do), the RPG elements are surprisingly deep and make for a nice big experience.
Plus, the game's on sale for just a buck this weekend, so if you have any interest in playing this one at all, it's more than worth a try.