On my Vista (SP2) machine, I can do this:
1 - Start -> Run
2 - Type anything, let's say "C:\"
3 - The correct window appears
4 - Start -> Run
At this point, the dialog is empty! In other words, it does not remember my last selection.
However, if I begin typing a command, it does start to auto-fill my previous entries, so the MRU list is preserved somewhere.
Does anyone know how to restore the default behavior? I'm not sure what I've done to cause this problem, but I assume it's a registry twiddle somewhere.