We've looked at a lot of 3D apps before, but I believe that HoloToy (US$0.99) is really something special. If you have an iPhone, iPod touch, or iPad, you should download it right now. I don't think you'll find a better 3D app in the whole store.
HoloToy uses anamorphosis perspective projection to do its magic. This means that you won't have to wear those cardboard anaglyph (usually red and cyan) glasses; aside from being annoying, they kill the brightness and reduce colors to a muddy shade of beige. All you need to do is look at it and twist and turn your device to see the effects. It's an interactive app, and by making wonderful use of the built-in accelerometer, you can do a do a variety of things, including moving around a HoloBot robot and even playing a few games.
The process used prevents images from appearing in front of the screen, so what you get is a five sided box, with the screen being a clear wall that you look into. Twisting, turning, and tapping on the screen lets you interact with all of the 3D images.
The intention of the app was to start with a few sample images and add others every week or so, based on reader feedback. In fact, just today an update was released adding a customizable aquarium option. You can see the progression of the app as the new images have been released; the app started as a bunch of planets suspended in space that you can spin around by swiping. The distance between the planets and the back wall is apparent, and there is a white box on the back wall whose corners you can see by twisting and turning the screen. The depth effects get better with the next two non-interactive modules, an impossible triangle and two differently sized boxes.