Favicon is the icon that appears next to your Website URL in the browser address bar. A favicon is usually your blog logo. There are many free services that help to create favicons for you but most of these services use still images.
Here i'm going to show how to create an animating favicon.

Creating Favicon

1.Go To FaviconGenerator
2.And just at the bottom of the page upload your blog logo or any icon you wish to make as your favicon and also add your blog title as the scrolling text. You will find all the help at favicongenerator
3. Hit the Generate Favicon Button and you will be taken to this page,
Here you will see many images just right click the animated one and save it to your computer.
4. Now upload the image to any image hosting website.

Adding Favicon To Blogger

1.Go To Blogger > Design > Edit HTML.
2.And Search For and just above it paste the code below
<"link href= ' ADD YOUR FAVICON LINK HERE ' rel='icon' type='image/gif'/">
3. Replace ADD YOUR FAVICON LINK HERE with the image URL of the favicon you got from the image hosting website.
4. Save your template and you are done!
View your blog to see it in actionon the address bar and tabs.