In my iPod Touch I have:
WBaduk to do the free problems they have (offline support added recently)
Goban, Sente and Nihon-Kiin's Free as virtual boards
Champion Go Crazy Stone to play 9x9 games (I have a 2nd gen iTouch, it's too slow to play quick 19x19 games)
GnuGo (removed from app store a long time ago)
Dragon Go Server to play in that server, although the web interface is good enough (turn based)
A shortcut to LittleGolem mobile version, to play there (turn based)
SmartGo Books, to read something (currently Sakata's Suji and Antisuji of Go)
Tsumego Master by the Nihon-Kiin, I bought the intermediate kyu problem package
if I had a newer iTouch (I can't upgrade from iOS 4.3, too old), I'd also have Yoo Chang's Tsumego (search for SGData in the app store). I have checked it in my iPad, there's a free version and problem packages
in my iPad I have (in addition to the previous, when available)
SmartGo Kifu: the best app overall
iGoban as a virtual board (one of the nicest boards all around)
Igowin HD: to play against the iPad
Crazy Stone: to play against the iPad
Wbaduk: to play online, problems are done in the iTouch (Koreans are strong!)
Tygem: to play online (Koreans are strong!)
Panda-Tetsuki: to play online (have not played with it yet)
Note: I have both Igowin HD and Crazy Stone. I must say that since both play different (very) from each other, this is not a redundancy. I like Igowin better to gauge if I have improved, and Crazy Stone to play hard 9x9 games. Both are excellent.
I'm always on the lookup for new apps for my iDevices

Edit: forgot two online playing apps for the iPad