I have a similar problem to one posted 22/7/08 solved by Alias but mine
still happens.
MS Outlook continues running as a process when terminated as shown by Task
Manager; it disappears from the Applications tab but remains under the
Processes tab.
If Outlook is reloaded, two copies appear under Processes (albeit the second
with only small memory usage) but nothing under Applications.

If the two copies are killed (End Process in Task Manager) and Outlook is
then reloaded again, I'm informed that Outlook failed to load properly and
do I want it loading in Safe Mode now. Outlook loads successfully in either
mode, but still leaves a copy of itself behind under Processes when
terminated.

This is all running under Windows XP Pro SP2 and Office SP3. I have norton
360 but this problem didn't happen just after this.
Have moved the pst file to other computers and exported it but doesn't
occurr there so appears related to Office 2003 on this computer. Similar non
terminating occurrs with winword that has multiple cppies running as
precesses but function is not affected.
Did what was suggested and removed Addins from
"Tools/Options/Other/Advanced Options/Com Add-ins or Service
Options?" (including "Itunes Helper") no help. Rebooted twice.
When I reboot or terminate the extra outlook processes outlook opens. If I
try to open outlook a third time without doing above it fails and anothing
process starts.
Don't use the animated helper? Do not have Junk Mail and Deleted Items empty
automatically.
Do have autobackup but present for 12 months no issue.
Please help re something else causing non closure.
? remove ittunes ?
Nick