Animated gifs can be very cool. However, like many flashy things on pages, they need to be used sparingly, and shouldn't be too large.

Remember that when you load an image, you're just loading that specific image. But when you load an animated image, you're loading as many images as there are frames in the animation. So when you create an animated image, you have to keep it small (because more pixels means larger size) or reduce the number of colors (because the fewer colors, the less memory the image takes up, and therefore loads faster). Here are some examples of animated gifs which are not too burdensome.

However, notice what happens when you're trying all these images at once. If you're on a computer with a slower processor, the animation doesn't work very well when there are several animated images on the same screen. Also, all of these gifs are reduced color images. They don't take up as much space as some images of the same size, because they don't take nearly as much space as full 256-color gifs.

My own personal advice is that animated gifs can look good, but should be kept to one per page, and shouldn't be more than 50k (even that is really pushing it). I use one of these images as the header for my fractals page, and even then I'm thinking sometimes it takes too long to load.