Hi Peter,
If your using Windows Media Player 9 this can be done by going tools >
options > Privacy Tab. At the bottom you will see buttons to clear the
history and stop saving url/file history.
For WMP 8 or 9 you can remove individual items from the list by going to
start > run > type in regedit
Then manually remove the file names in the right pane from
HKEY_CURRENT_USER\Software\Microsoft\MediaPlayer\Player\RecentFileList
To prevent WMP8 keeping a list navigate to
HKEY_CURRENT_USER\Software\Microsoft\MediaPlayer\Preferences
In the right pane fine AddToMRU, Double click this and set its value to 00
Hope that helps
Mark