@Grumly: You can try that one for free, although if you want the full 600 exercises, you have to make an "in-app purchase" for $2.99.
Chess Quest includes twice that many puzzles for the same price, but it lacks some of the fun elements of Chess Trainer: rankings, personal ratings graph, dogs playing chess, etc. :)
This may be outside the topic as apparently this app does not allow you to play live games, but has anyone tried ChessTrainer on Iphone ?
I have seen a video here
http://www.mychesstraining.com/
and I don't know what to think about it