Movement is a tricky challenge to design and capture. The deep integration it has in our everyday lives is easy to overlook, but when it is wrong, it becomes the prima donna of the show. Sometimes, words are not enough to explain it (see janky, shifty, bubbly, laggy (?)).
This article (found by Stephen) describes the important of animation not becoming the main focus, but a way to support the user experience. If a fade out will encourage the feeling of taking away or a popup comes from the source to show the hierarchy, then animation is a great tool to design a great product.
What are some of your favorite animations seen in the wild?