Windows IE History Cleaning and Removing Unplugged Network icon from tray

Remove history in internet explorer address bar

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.

Remove A network cable is unplugged icon from tray

Click on Start>Run..., type regedit.exe and click OK. Delete this key:

HKEY_CLASSES_ROOT\CLSID\{7007ACCF-3202-11D1-AAD2-00805FC1270E}

Restart to apply the changes. I haven't had any ill effects so far. Make a backup of the key just in case (select the key and click on File>Export...).