You may have heard about "incognito mode" in Google Chrome or "private-browsing" in Mozilla Firefox. In these modes browsers do not save anything to the hard drive, cache, cookies, etc. After exiting this mode all activity is cleaned up.  One interesting bonus you get of these features is login into different accounts at once.

Personally I like Chrome behavior better, comparing to FF.  It just opens the new window allowing other tabs be active. My tip is more Chrome related.

In case you are already logged in into some account like Gmail, Dropbox, etc.. and want temporary to check other account on the same service, just open "Incognito window" do all stuff and close it again. Because cookies are separated you will be allowed to do so without logging out of current account.

This also is useful when needed to login into same web program as two users simultaneously (user and admin) while debugging or so.

With FireFox it is possible by create second account, see user profile