Surveys show that some people out of 100 like animated graphics, and some don't. (In case you haven't figured it out, I just made that up.) In other words, animated graphics, or .gif files that display motion or animation, are to be used wisely. If you're thinking of adding animated graphics to your site, do so with caution. Too much movement can distract users away from the other content on the site, and that is annoying for any user and web publisher. Plus, animated graphics mean bigger file sizes.
Another caution is to remember browsers that don't display the animation. Since the animation is really comprised of several .gif files combined into one, and not all browsers have .gif animation viewing capability, you need to think ahead. Use a starting .gif (the first graphic in the series of graphics that comprise the animation) that will display the needed information or look for the page. Otherwise certain users won't understand or see what you as the web publisher is trying to convey with the animation.
This may not happen often, but there are those who still use old browsers. Be considerate of your visitors.