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