Does anybody know how to set that little icon which precedes the URL in many websites such as this one?

add the foll code to the head part

<link rel="SHORTCUT ICON" href="favicon.ico" />

make sure you have a favicon.ico file and make sure the path is right.

Awesome, thanks for that - do you happen to know the size of the image?

16x16px

I dont add the <link> tag and it works perfectly in firefox.
Not IE tho...but that doesnt matter.

IE6 doesn't display it in the address bar, but it does display it in the favorites... (probably because it's a FAVoritesICON...)
IE7 displays it in it's tabs, however.