If you haven't bought the device yet, I would suggest getting a Kindle Fire. They are cheaper, easier to manipulate, and more durable. My youngest (severely autistic) has an iPad that he uses at school for communication, and it's had to be repaired 2 or 3 times over the last couple years, where as the Kindle hasn't had any issues at all.
Other than that as far as apps there are a ton of them. For fun though I recommend getting Angry Birds - my son loves that game. It's easy for him to understand and play, though some of the upper levels are challenging, he still has a lot of fun with it.
For free (or fairly cheap) learning based stuff...
* Preschool and Kindergarten Learning Games by Kevin Bradford
* My first puzzles HD by Alexandre Minard
* JumpStart Preschool Magic of Learning By Knowledge Adventure
* Happi Reads by Happi Papi
* My first words: the complete collection by Alexandre Minard
If you need a communication type program...
* TouchChat HD by Silver Kite ($150)
* Proloquo2Go by AssistiveWare ($220)
* TapToTalk by Assistyx LLC (app itself is free I think, but if you want full access you have to pay through their website for the additional upgrade packs $180)
iPad as better as they are bigger and also you only pay once. With iPhone you might have a contract. On iPad there are a bigger variety of games to play. When you do decide which one to get, this website has a list of good apps for autistic children. http://www.autismspeaks.org/autism-apps. Hope this helps. ;)
Teachers and doctors are using iPads as a tool to reach out to children with Autism or Asperger Syndrome and the results are remarkably great. Autistic children are showing tremendous improvement after playing fun-filled exercises on iPad which is less stressful and more fun for both the teachers and the students. Below is the list of 10 best iPad applications to give Autism a voice.
Proloquo2Go – A must have app that provides you with a full-featured augmentative and alternative communication solution for autistic children who have difficulty speaking. It contains text-to-speech voices, up-to-date symbols, powerful automatic conjugations, a default vocabulary and much more. Proloquo2Go is considered as a good alternative against buying an expensive AAC device. Even SLPs, teachers and parents recommend it for children and adults with autism, cerebral palsy, Down syndrome, developmental disabilities, apraxia, ALS, stroke or traumatic brain injury. Proloque2Go app for iPhone and iPad is available for $189.99.