From Sheila Bigel:

This came up at the CFCS meeting. Took a quick look at Internet Explorer 8. When you select an item in the dropdown menu there is an option to delete it at the right side.

Added by Hewie:

I checked FireFox. If you click the down arrow in the address bar, it will show a list of previous locations. Scroll down until you get to the one that you want to eliminate or just start typing the URL and when the list of possibilities pops up, scroll to the one(s) that you want to eliminate and “Delete” it. With it highlighted, just press the “Delete” key and it is gone.