Windows Media Player 8 (or higher) has the annoying habit of retaining the names of the latest files and read the display in the "File" menu. This information must be stored in the registry. This trick will allow you to remove the traces of these files and to prevent the addition of new data in this list.

We will first start by deleting the entries corresponding to the latest files played by Windows Media Player:

Run regedit (Start menu, select Run ... and type regedit)
Go to HKEY_CURRENT_USER / Software/ Software / Microsoft/ Microsoft / MediaPlayer/ MediaPlayer / Player/ Player / RecentFileList. In the right pane of the Registry Editor, delete the key type File0, File1, File2, etc..

Do the same if the file handling RecentURLList is present (corresponding to remote files read by WMP).
We are now going to prevent Windows Media Player to add new files in the list:
Run regedit (Start menu, select Run ... and type regedit)
Go to HKEY_CURRENT_USER / Software/ Software / Microsoft/ Microsoft / MediaPlayer/ MediaPlayer / Preferences Preferences
Create a new DWORD value named AddToMRU and give it the value 0

To remove this update, simply delete the key AddToMRU or increase its value to 1.

That is, Windows Media Player can store the names of your files, people with access to your PC no longer be able to view the latest files viewed o) Note that the last open files with Windows Media Player will still be visible in the Documents menu on the Start menu, you can use the trick Empty menu documents leaving Windows for peace of mind.