Animated gif’s have a pretty bad wrap in the web design world. Mostly because when computers started being used by the masses everyone thought that it was very cool to be able to have images move. Thus everyone who made a webpage wanted at least 15 of these images on their website. I know most of you remember the days of geocities and angelfire and other poor websites. Here is a great example, please notice how distracting it is that everything moves.
Although animated gifs have a bad wrap, and now you know why, they can be useful in many circumstances. For example, they can be used to show more information in a small space; this technique is often seen in advertising. Ads are a certain size and only so much can fit on it. However if done tactfully you can use the real estate to show quite a bit of information in an animated gif. The problem here of course is that if all the ads on the page with yours are also animated then you have yourself a gaudy page.
Another situation where they are useful is if you use them to display several images that fall under the same category. For example I used one recently on a site to display the craftsmanship of a home building company. It rotates through images at a slow rate and is hopefully not too distracting as it is the only movement on the page.
The moral here is that not all animated gifs are bad. But I caution you greatly on wanting them on your website, use them sparingly and in good judgment or don’t use them at all.

Annoyingly Cute

Acceptable if it is the only movement on the page