Each type has it's own advantages and disadvantages. First there was animated gif files. This is fine for small animated icons or banners. You can also add a little movement to your pages using animated gif's as long as you don't overdo it. Then there were movies.
Movies come in a variety of file formats.
A few of which are .mov, .avi .mpg and .fli. There are at least a dozen others that do the same basic thing. The problem with movie files is the huge file size. They do have their place in the business world such as placing as a trailer on a powerpoint presentation. With the advent of dhtml code and javascripting, you can add movement to your pages by using graphics as what is called a sprite.