I know I shouldn't be using this application! But should I do so, and wish to delete the log of recently opened files. The quick and simple way is to delete the prefs file, located in your user's Library -> Preferences folder, and it's called Windows Media Player Prefs. Unfortunately, you do lose your entire prefs file, but who actually uses WMP enough to really want one?
Another way, of course, is to open new file names under WMP until the file you wish to hide any evidence of is pushed out of the list.
[robg adds: Here at hints, our mantra is not to wonder why one might, but merely to explain how one might... :) ]
Mac OS X Hints
http://hints.macworld.com/article.php?story=2004092022054789