iOS (jailbroken): Apple has some pretty smooth animations built into iOS, but if you really want to get fancy, DisplayCandy adds tons of new ones to the open, close, and switch functions of your iPhone.
DisplayCandy lets you choose from 12 different animations, like a page curl, a ripple effect, or a rotating cube. You can apply them to three different actions on your device (open app, close app, and switch app) and even customise the speed and direction of the animations. Remarkably, the custom animations work without any noticeable lag, at least on my iPhone 4. It's just one more great way you can customise your iPhone inside and out.
DisplayCandy is a $US2 download and is available in Cydia.