I noticed on my latested XP install that whenever I shut it down, a dialogue window (or 2 or 3) would pop up asking if I wanted to close IEXPLORE.EXE, even though I had terminated all my IE windows.

This is an undesirable program. This file has been identified as a program that is undesirable to have running on your computer. This consists of programs that are misleading, harmful, or undesirable.