How do I prevent Internet Explorer's address bar's URL history from showing up in the Run dialogue? No tweak seems to prevent this. I'm running Windows 8.
I am not sure if you can hide only the internet explorer history, but this is the way to prevent storing recently opened items:
Go to Control Panel > Appearance and Personalization > Taskbar and Start Menu. Click the Start Menu tab. Under Privacy clear the "Store and display a list of recently opened items in the Start menu" check box.
If you would like to remove one entry you can do it by deleting the item using Regedit, the key is HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\RunMRU
Hope that helps!
After looking into this a bit, my conclusion is that on 8.1 it's not possible to prevent IE history URLs (and Explorer history items, for that matter) from showing up among the Run Dialog items. First, I haven't found a fix, and second, the text hardcoded into the GUI ("Specify the name of a program, folder, document, or internet resource." - translated from German) suggests that it's not designed to be configurable what makes enters the Run Dialog:
(I cannot be 100% sure that the text is indeed hardcoded into the GUI. It could be conditional on some configuration state as to what enters the Run Dialog history. However, there is no such configuration option anywhere to be found.)
However, if you click the downwards pointing arrow on the right, you'll see the list of manually entered commands, without any IE URLs:
It doesn't seem possible to make this shortlist show up just by keystrokes without resorting to the mouse.
If you want to remove entries from this list, see spacebiker's reply on this page.