No-History Browsing: Check your browser History
How can I clear the address bar?
You've cleared your history, deleted the cache, removed all suspicious cookies... but still you can get caught surfing forbidden sites by your lowly address bar!
Address Bar:
You have probably already seen how the address bar in most browsers will display a dynamic drop down menu in anticipation of the address you may be typing. These items can reveal secrets. They are simple enough to remove, simply use your arrow keys to select the ones you wish to remove and hit the "DELETE" key. Done.

Turning this feature off in IE:

Make sure you have the "Content" tab open as shown above, then click on "Settings". A dialog will open like the one below:
You can then turn off the auto-complete feature. Far simpler is to install a browser like Firefox where you can add plugins and addons to do all of this automatically and very easily from a toolbar.
Firefox:
In firefox, this works similarly, that is, you can delete entries in the auto-complete address bar manually by typing in a few letters and then manually deleting the offending sites by selecting them and then clicking DELETE.
If I clear my history, does it clear my address bar too?
No.
Also bears repeating! Someone could type through various letters of the alphabet to see what pops up in your address bar. On the other hand, you could also snoop on someone else by doing the same.