Although a number of interactive children's books have billed themselves as being pop-up (or pop-out) books, like The Tale of Peter Rabbit and The Night Before Christmas (both from Loudcrow), nothing really popped up and constructed the 3D scenes that I remember from my childhood. Grimm's Rapunzel - Interactive Pop-up Book from Ideal Binary (US$1.99 for now) does just that, and beautifully. It's a universal app that makes full use of the Retina Display of the iPhone and iPod touch, and it looks and plays gorgeously on an iPad.
When you start the book, you are presented with a profusely illustrated book similar to the one used at the start and ending of Walt Disney's Snow White and the Seven Dwarfs. The book opens, and a text and picture page is displayed where nothing moves, ... but turn the page and the book shifts horizontally as the scene springs to life. Using physics that feel just right, objects bounce up and form a scene where you are given a clearly described task to perform. Each of the pop-up pages contains an activity ranging from sowing and watering seeds to helping Rapunzel find her sheet music and harp. When completed, each activity pays off with a character thanking you or providing reinforcement, like Rapunzel playing a little tune on her harp. Touching objects on the pop-up pages causes things to bounce a bit, which is common, or add a few surprises; for example, when you touch a candelabra, it lights up.