To clear the list of recently used files, and not mess with the user's settings, the following code will work:
originalSetting = Application.RecentFiles.Maximum
Application.RecentFiles.Maximum = 0
Application.RecentFiles.Maximum = originalSetting
This will remove the recent files and then reset the maximum number of recent files back to whatever the user had initially.
If you just want to remove them individually, you can step through them in reverse order to get the job done.
Dim i As Integer
For i = Application.RecentFiles.Count To 1 Step -1
Application.RecentFiles.Item(i).Delete
Next
You need to run from the bottom of the collection up, because as soon as you delete one of the entries from the RecentFiles collection, all of the indexes of the remaining files change. This way, each time through the loop, you are deleting the last item in the collection.
And also, since this collection is Base 1 instead of Base 0, the last item in the collection is Application.RecentFiles.Count rather than .RecentFiles.Count-1.
I just love all those little inconsistencies in Excel.. :)