Not necessarily educational but lots of fun.
Itsy Bitsy Spider is a fun early preschool app. It was a big hit with my kids when they were 2. The music isn’t terribly annoying and there aren’t any in-app purchases. $1.99
The Fantastic Flying Books of Mr. Morris Lessmore
is an interactive book about books. I’ve had this for three years already and my daughter still loves it. This app is iPad only, however. But well worth buying. No in-app purchases. $4.99
Talking Tom or Talking Larry. Take your pick. Mindless fun. A very fond memory is of my daughter, almost 3 at the time, having a full blown argument with Talking Tom. Both are $0.99 and you can have some in-app purchases.
PBS Kids is where your child can watch clips of all their favorite shows. It does require an internet connection but no in-app purchases, and no cost to download.
Monster at the End of the Book is a fun Sesame Street app starring Grover. Kids can break down walls and untie knots to keep turning the page to get to the end of the book. No annoying music and no in-app purchases. $4.99
The Ragged Mommy 