This very simple solution applies to a narrow cross-section of the "needs to close" variety.
In this case, the full message in Event Viewer was in applog, Event ID 1000:
Faulting application iexplore.exe, version 8.0.6001.18702, faulting module msxml3.dll, version 8.100.1052.0, faulting address 0x000a1425
Original message was in French:
Application défaillante iexplore.exe, version 8.0.6001.18702, module défaillant msxml3.dll, version 8.100.1052.0, adresse de défaillance 0x000a1425
My user was on a fully patched Windows XP SP3 PC. One Windows update had been installed the previous evening, KB973904. Uninstalling it sped up IE performance, but did not solve the problem of the error message.
Uninstalling and reinstalling IE restored functionality to the user's web-based applications (some Flash and Java), but the error message still appeared when opening a session in the web-based app.
Solution: the error message was ultimately eliminated by going into Add/Remove Programs and repairing MSXML 4.0 SP2 (KB954430).
Hope this helps someone else out!