I was under the impression that favicons need to be icon files (.ico) that needed to be uploaded and linked between your sites head tags. Then I spotted this dancing animation in my browser url bar and firefox tab…
I was visiting the Digital IT Blog via a site tracker referrer link when I spotted this animated gif that they had used as a favicon. Out of 15 open tabs, that was the only tab that was drawing my attention repeatedly.
I checked out the page source code and found that they had used this animated dancing gif to link in the favicon shortcut. The size of the gif image was a huge 183kb (my favicon is only 2kb) and it took time for all the gif frames to load. But you instantly saw the first frame in the favicon and over a few more seconds the dance started further drawing your attraction.
In modern tabbed browsers favicons are displayed on tabs, and while users open multiple tabs easily, drawing their attention with animated favicons can be useful to get them to visit your site first. Some might say it is obtrusive and distracting. But I think is a tip you might just consider if it fits your site.
Update: Such image favicons do not work in IE as pointed in comments. So it is better to stick to .ico icons. Unless you can configure a script to detect the browser and accordingly decide which favicon to use.