Role Playing Games (RPGs) are a staple of computer game consoles going back to the beginning of computers. The ultimate expression of an RPG, to me, is the action RPG: One that combines fighting, storytelling and questing in one. These RPGs are among the best I've ever played on any platform.
Chaos Rings ($12.99) is a game that's played by two whole different teams of characters. Square Enix's expensive RPG is a very deep game with an emotionally tense plot and great character development. The main feature of this well-told story is due to to the game's unique character interactions and expression interface used in cut-scenes, plus a wonderful and large overall set of conflicts to be resolved between almost everyone in the game. There is a lot of talking and emoting going on here.
The item and skill (called "Genes" in-game) trees and overall player improvement schemes are more in-depth than most games I've played on any gaming platform. Those improvements are also dependent on combat outcomes. This game would be a delight to play on the iPad also because of the beautiful art design of the overall game. For a visual demonstration, check out Erik Fikkert's video review here.
Hero of Sparta ($1.99): "Epic" is the word for this "300"-style Gameloft RPG. You fight from the first moment of this game and there is more focus on combat here than any of the other RPG's I've played. Your Spartan has awesome finishing moves, and he needs it in a world where his AI opponents can fight in quite real-world ways: surrounding him, holding him, lifting him, stabbing him in the back for greater damage and so on. This game is a Greek-geek hack-n-slash-fan's dream! It's among my favorite iPhone games, especially for the price.
Across Age™ EX Unlock ($4.99): This is a review of the upgraded (via in-app purchase) Across Age™ EX game. I found this to be the epitome of a whole sub-genre of iPhone Zelda-style games, I liked this one for it's polished controls, compelling storyline, and the excellent team features. I confess to not being the biggest fan of this type of Japanese-style Action RPG, but there are plenty of people who are, and I found this type to be the most popular among RPGs I had to choose from.
Ravensword: The Fallen King ($4.99): I enjoyed this game due to its difficult monsters, an interesting side-game that helps earn money and the fact that the quests are challenging in general. It is of a more traditional dungeon questing/grinding style RPG where nearly all of your missions are determined mostly by following quests given by non-player-characters (NPCs). While the 3D environment is well done and the monsters, buildings and NPCs relatively well-rendered for an iPhone, play is fairly slow due to the large environment and very predictable and repetitive monster spawning. Additionally, the control scheme is in dire need of another d-pad. Fans of the progressive rock band Rush note: Free healing can be had in the cemetery at The Fountain of Lamneth!