This has been bothering me for a while, but not nearly enough to do something about it. On my multisite network, the admin area of my sites have taken the favicon of the main network site instead of the sites which they are an admin area for.
So I set about writing a quick function to rectify this. The following snippet sets the favicon for both your main site and admin area, where the favicon is a file called favicon.ico stored in your active theme folder:
If you wanted separate favicons for your admin area and your site, you can create two similar, but distinct functions, like this. Note the two different image links: