While using Firefox 3 to work with a web application that uses basic authentication for access control earlier today, I wanted to be able to log in to the application as a different user account without needing to close and restart Firefox in order to get it to stop automatically resending the authentication data from my original login. (After logging in to a site via basic authentication, Firefox will automatically continue to resend the credentials from that login on any subsequent requests to that same site, until the browser is shut down.)
After hunting around for a while looking for a Firefox extension that would do this, I discovered a way to do this built into Firefox itself: In the Tools menu, select Clear Private Data; then in the Clear Private Data dialog that appears, check the Authenticated Sessions checkbox, clear all other checkboxes, and click the Clear Private Data Now button.
This will get Firefox to "throw away" its saved basic authentication credentials from the current session, and allow you to log in as another user, without having to close Firefox. I've found this to be handy when I have a lot of Firefox tabs open, and don't want to shut down Firefox (and close all of my open tabs in the process) just to "log out" of the basic authentication session that I have open in a particular tab.