Aside of the problems with flash ...
Is it also not a reaction of the visitors that the web designers want to avoid: the more it moves, the faster the visitor looks for the back button ?
You have other options: transitions in css is about the first I come up with, but other options exist as well such as svg animation (yeah, "that" browser won't do svg to start with)
CSS3 transitions: [w3.org...]
SVG animation: [w3.org...]