My 20-month old niece has really liked the following two apps. One is free and one is paid.
Disney's Toy Story Read-Along (Free)
This is a really well designed read-along book with great visuals, a built in text reader to read the story, and a few interactive features built in on some of the pages. It has great music, a few animated clips from the movie, and an easy to use interface. My niece was able to turn the pages herself!
Elmo's Monster Maker ($3.99)
This app is actually designed for the iPhone and iPod Touch, but it translates extremely well to the larger iPad screen. You can create your own muppet monsters by adding eyes, hats, and noses to several muppet body options. Once the muppet has been created, you can take a picture of it, have Elmo interact with it, and even watch it dance. My niece more enjoyed watching me activate the features, but she was able to touch the eyes and nose area of the muppet to change the muppet parts.
Header photo by Robert S. Donovan