If you want a favourite icon, here is how to do it. You can see the favicon in your web browser and if you create a desktop shortcut or add a site as your favorite. Here is how it look like in Internet Explorer 7.0 in Windows Vista.
First you need to create the image that will be used and a simple way is to go to http://www.favicon.cc/ where you can draw your own icon easily.
Then you need to save this icon to your computer by clicking on the "Download Favicon" button and then upload or publish it to Internet somewhere. One place I know where you can upload the ICO file is at http://skydrive.live.com. If you use the website favicon.cc they have the option to "Publish under an open license" but this method does does not work for everyone.
Now you need to add it to your blog or site.
If you have Blogger click on the Layout link on the Dashboard. Then click on Edit HTML.
Now you need to find </head>. You can press CTRL+F and enter </head> to easy find it.
Before </head> place the row below that is in bold and you need to change 'http://favicon.ico' to the location of your favicon.
<LINK REL='SHORTCUT ICON' href='http://favicon.ico'></LINK>
Here is an example what it look like when ready.
Now click on SAVE TEMPLATE and you're done.