On my old blog I had a favicon, which I somehow created with som hassel (foregotten now) and I wanted it on my new blog here at blogger.com. It turned out to be real easy because in Template -> Edit HTML it justed added the link in the HTML header like
and voilá it's there. I had to google for the needed markup.
I would prefere to place the favicon external on ex. picasa, but since it only accepts jpeg and gif that's not an option. I don't think it's a real problem since it'll probably be cached by browsers and shown when my server is offline.
Wikipedia has a nice description of Favorites Icon.