If you want to tell a whole story in a web graphic, but have only a limited area of pixels to play with, what do you do? Show a video? How about an animated GIF?
Animated GIFs save space. Moving images save space because they can say a lot while running on the spot. In fact animations can say quite a bit without even adding any text. Facial expressions and body language can say it all.
Video does of course use the power of body language and the moving image. Video occupies only a small part of the page, unless of course the viewer chooses to watch it full screen. Yet animated graphics give more creative freedom. Flash animations and animated gifs are better suited than video for logos and web ads.
Drawn animations can also be clearer and sharper than photographic images at very small sizes.
Flash animations do have the disadvantage of not being universally viewable. One answer is to make animations in Flash and save them as animated gifs.
A word of warning. It's all too easy to get carried away by the charms and advantages of cartoon style animation! To come down to earth, it's as well to remember that an animation running too close to text can be distracting. The viewer can play or stop a video at will. You can't always do this with a banner or logo.
Of course a banner's aim may indeed be to distract you, luring you away to press a button to exit to another page. Trouble is, it may only succeed in annoying.
If your graphics really insist on getting up and dancing, make sure at least that they steer clear of the text.