Do you want to remove the address bar completely or just have it not keep any history? To remove the address bar completely you can just click view -> Toolbars and uncheck address bar. There is probably a setting in gpedit.msc that will prevent someone from re-enabling it, though I've never looked for such a setting.
 
To keep IE from keeping a history just look here http://www.google.com/search?q=clear+ie+...tart=0&sa=N
or from the control panel go in to Internet Options and click clear history on the first screen when you just want to get rid of your history.

If you just want to stop autocomplete for addresses:
At the top of your Internet Explorer select "Tools".
Select "Internet Options" from the drop down menu.
Click on the "Content" tab at the top of the Internet Options window.
In the Personal Information area, click on the button "AutoComplete..."
Click the check mark for Web Addresses so it will be unchecked.
Click "OK". Then click "OK" to close the Internet Options window.

Actually need to clear the forms. That's the spot where I do it though. Thanks.
 
I am cleaning any personal data from my laptop to send it for warrenty service.