Windows 7 how to purge entries in Run command window

1. Open Taskbar and Start Menu Properties by clicking the Start > Control Panel > Appearance and Personalization > Taskbar and Start Menu.
2. Click the Start Menu tab, and then, under Privacy, clear the Store and display a list of recently opened programs check box.

Source: Clear the Run history on the Start menu at Microsoft.com.

The entries are stored in Regedit

Open up regedit.exe through the start menu run box, and then navigate down to the following key:

HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\RunMRU

You’ll see all your recent commands on the right, and you can delete any of the keys that contain your commands. You’ll have to logoff and then back on, but the list should be clean.

But since a standard user cannot modify the registry, the best option would be not to save the information in the first place, as explained in the previous answer by @CharlieRB.