GIF and Flash animations have their place on the web when used sparingly to direct attention for a specific purpose.
On this page, there are several animations running all at once, as a showcase. Having more than one animation (or slideshow, or video) running at the same time is not a good idea for a typical webpage, because it’s distracting, and in many cases, annoying.
Below, the website header for ProcrastinatorsCalendar.com only runs its animation once, when you first visit the site (otherwise it distracts from the body of the page.) However, the example of it on this page is set to repeat the animation continuously.
The animated GIF logo (to the left, below) was already on the Motorcycle Road Tours site, so when I did a complete site overhaul I also rebuilt the logo. I didn’t have any of the original design files, so I had to rebuild everything from scratch. It seemed silly to me to have a riderless motorcycle dashing across the logo, so in my reconstructed version the motorcycle has a rider
The extra “imagiNed Web Design” touch that thrilled my client was that the tiny motorcycle and rider now riding across the logo was the client on his own motorcycle.
To take things one step further, the Motorcycle Road Tours homepage homepage has the logo actually riding down the winding road of the website header. That’s another animated header example.