I had my doubts about whether my 3 1/2-year-old daughter would like this app, but I was completely wrong! Every night she has requested it and every night she has phone asleep within 10 minutes of starting the app. My only complaint is that its too easy for her to get accidentally into the App Store.
Mom to Char about Bedtime Story: an animated Aesop Children’s Book for helping children to sleep, v1.6