Animations, generally speaking, are overused and annoying - the mark of rank amateur design. The basic rule for web design applies here: just because you "can" does not mean you "should". Animations should be used only to get a point across. More than one animation on a page is just plain bad design…unless the point is to entertain a small child.

This is a good example of a webpage with many animations, as well as a number of other flaws (flashing colors, bad text design, an annoying Flash movie, etc.)

Here is one of the few animations on the web that really work.