Rachel Hinman has written a great primer on the use of animation in UI design:
Transitions and subtle motion-based animations are emerging as a new and compelling mobile design material, worthy of being learned and being used with efficiency and grace. The addition of movement to a mobile experience can provide clarity, information about context and, frankly, a dash of joy and fun. However, too much animation or funky transitions can destroy a perfectly good mobile experience. This makes understanding the guiding principles behind the art of animation the best first step to artfully applying motion to your design work.
She goes on to demonstrate how each of the 12 basic principles of animation can be applied well in user interface design. Recommended for any UI designers not already familiar with the 12 principles.