The VMWare Player does not include an option to clear the list of "Recent Virtual Machines" (why not?!?!). Since the list of virtual machines that I had opened was growing quite long, I set out to find a way to clear it myself.
After searching in a few places (Windows XP), I came across the file that holds this information. It's called preferences.ini and is located in:
[drive]:\Documents and Settings\[user]\Application Data\VMWare
UPDATE: In Windows Vista, the file is located in:
[drive]:\Users\[user]\AppData\Roaming\VMWare
At the bottom of the file, you should see entries like (where X is a sequential number):
pref.mruVMX.filename = "..."
pref.mruVMX.displayname = "..."
Just delete/reorder the entries as desired, save, then start VMWare Player to see the changes. VMWare Player will need to be closed before you make the changes, or they will not be saved.