This will be an ongoing list that I edit and add to as needed:
Injini - I got the lite version, then upgraded. My son needed an app to work on puzzles, tracing, and other fine motor activities. This one is perfect because of the simple, appealing graphics, ease of use for a young iPad beginner, and increasing complexity. He comes back to it again and again.
NatureTap - perfect for my son's avid interest in exotic and scary animals. I like that it has some games too and more things to purchase if you want. I signed up for the insects and spiders, and purchased the reptile pack. It comes with some free birds.
iBird lite - beautiful and fun, not a game but more like a gorgeous book