Some of our favorites, (DD6&7):
Educational:
Mathmateer (formerly Rocket Math)
ABC Mouse (Zoo and Grand Canyon)
Khan Academy
Monkey Preschool Lunchbox and Monkey Mathschool Sunshine
Math Blaster
Schoolhouse Rocks videos (from iTunes, not app store)
Super Why
Puzzle/Thinking Skills:
Cut the Rope
Where's my Water (Where's my Perry?)
Flow Free
Draw Something (DD7 plays with me and some relatives)
Scramble with Friends and Words with Friends (DD7 plays with me)
Entertainment:
There's a Monster at the End of this Book (interactive book)
Watch Disney and Watch Disney Junior (must have a participating cable service provider)
Any of the Toca Boca apps
Video Star
Go Swim (DD7 does Swim Team)
Pandora
Radio Disney
Fruit Ninja
Temple Run
I also have two ebooks that DD7 reads. One Winnie the Pooh book was free, and an American Girl book. We also subscribe to the Disney Family Fun magazine and you can get digital edition free with the mailed subscription, so that's set up in the newstand app.
In addition to the apps, whenever I get a new movie, I watch for sales on the versions that come with digital copies, so we have a dozen movies in our iTunes library that I swap in and out. Plus, most of the disney junior shows have at least one free episode, so I've got some of those also (we have a younger DD that likes those shows now).