I have an ipod touch and the whole family uses it.
Check out “RustyBrick” for a bunch of useful Jewish apps.
Also, for internet use, I use Mobicip which you can seriously lock down, just make sure that safari is turned off. There’s a surprising amount of parental controls built in, you can lock the ipod down pretty tight.
With that said, you asked for games:
my games:
bookworm
shanghai mahjong
kenken pro (sudoku)
kids games: (well, and mine too 🙂
flightcontrol
carcassonne
traffic rush
angry birds
fruit ninja
pictureka
I also use some helpful apps:
dropbox
mint.com
google earth
skype
wordpress
wikipedia
amazon.com
star walk
audubon society has a really nice set of apps based on their field guides, I have their bird application, which was expensive but VERY useful if you like to look up bird information, calls, etc.