Unless you are building a personal website, use graphics only when they are absolutely necessary. Avoid using fanciful animated graphics (e.g. animated GIF and Flash SWF). To give your reader a professional feel, use graphics only when it is required to illustrate for your textual content. However, you can use small logos and banners to liven up your website - remember, you want to give a professional impression to your visitors.
There are a couple of clever things that can be achieved with images:
Images which are in GIF format can be animated. The specific GIF format which
allows for animation is GIF89a.
Creating animated GIFs is really very simple. You need to create a small GIF
for each frame of your animation. This may result in several GIF files. Then,
use a utility such as GIF Construction Set
(Win95/NT, 1.2MB), to create a single animated GIF image from your separate
GIF files.
This is an example of an animated GIF:

Tips and Tricks
Some tips for creating web-friendly images: