I have an iphone, my husband has one, and my 8 yr old saved her money to buy an itouch. Needless to say I have spent way too much time playing with APs. My lists consists of APs we already had on my phone and some others that I searched. You can spend an unlimited amount of time searching so I limited my time to 20 minutes.
Here are some of the APs I found:
Math Drills Lite- flash cards
Alphabet Tracing for pre-k kiddo to practice his letter formation
K12 Timed Reading Practice- Help kids with their reading fluency using short passages that are timed
Shake'em Capital and States- a fun way to practice learning capitals and states by shaking it up on your iphone or itouch
Finger Physics- My 8 yr old daughter loves this game. You have to use strategy to figure out how to make the egg fall into the basket with out breaking. Each level gradually gets harder. Fun and strategy based.
We have itouches in our library, but haven't found the educational wow factor of using them. We really don't have time to play during the day, so we haven't used them. I don't think they are appropriate or doing research b/c the screen really is too small for multiple students to use much less one student be able to read the info on such a little screen.
If time wasn't an issue, I could see using them for math drills, working together like on the finger physics to try and get the egg in the basket, there are some board games that are math related that more than one student could play.