I use mozilla as my browser now, for about 2 months.  It is great.
BUt...I find I am still getting the most annoying pop ups from ms
internet explorer.  How can I permanently get rid of this problem??

Sounds like you have spyware or ie addons.

Quick fix (not too effective IMO)
-Download and run Spybot, Adaware, HijackThis(careful, HijackThis if
not used properly can mess up your registry and thus your system)

Long fix (but effective [I like this cuz it gives you a fresh running system])
-Backup important data, format hard drive, reinstall Windows.

I would add two more must-have freewares-- ccleaner.exe (from
ccleaner.com) and spywareblaster.

If you are using Mozilla and if you are not starting internet explorer
then there is no way that popup can come from IE.  it is only possible
if your IE is running behind.

If you make Mozilla as your default browser and rename your
IExplorer.exe to some IExplorer._xe which is there in program
files\internet explorer folder.

And there can be popups in Mozilla as well, you will need to upgrade
it. Even if they have made popup blocker, new popups can be invented,
they can not block it forever.

- Akash Kava
Our free IMAP/POP3 service at http://www.evenmail.com