However, any user that uses your computer can find out what addresses you typed in as well so some may be interested in clearing the address bar addresses.  Just clearing the browser history will not do this as a registry modification is needed:

Click on Start, then Run.
Type regedit in the box provided.
In Regedit navigate to HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\Typed URLs
Then just delete all of the keys that list the URL's you no longer want to see.

Note: Clearing the recent documents history from start menu properties will clear this list as well.