tChess Pro (version 1.7.3; $7.99) has been great on the iPod and iPad for my occasional chess study for more than a year. While I am nowhere near becoming a chess master (I'm currently rated 1806 by the U.S. Chess Federation, in the top 10%), I do take my tournament preparation relatively seriously. I think tChess Pro is probably quite good for casual players as well.
The http://www.tchessgame.com product website has pretty good information, and many substantial reviews can be found in the Apple App Store (where you may need to search for it as "t Chess Pro" instead of as "tChess Pro"), and elsewhere on the Internet. I wrote a review of some more advanced functionality here for my chess club's blog, which seemed a better place for that than here, given the review's more technical content.
