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!