Me again. So far we've tried a few, including "Henry and Hailey's Preschool Pals", "Koi Pond", "Dizzy Bee", "Scribble", and "Preschool Adventure". They're all nicely made, but so far her interest has been limited. Generally about 30 seconds of seeing it is followed by a demand of "another one!".
Videos, on the other hand, are a huge hit. We have some Disney and Pixar movies, and "Tigger and Pooh" (her favorite) and a couple other TV shows.
Anyway, she's still learning how to use the thing. We'll see how it goes as she becomes more adept with the touch screen. I think it's actually a decent fine-motor skills exercise; her first attempts are certainly somewhat clumsy, and something she can refine over time.
As expected, the hard part is getting the iPod back. Our first attempt at taking it away was, um, somewhat less than successful. It does suggest that it'll be a very effective time-waster on the airplane.
Thanks for all the suggestions, I will continue to report back as I learn more.