What OS (Win XP/2000, etc) are you using? Did you try doing an anti-virus scan in "SAFE MODE
"? Have you performed any anti-spyware scans?
If you do a Google search you will find numerous complaints of multiple instances of iexplore.exe running in Task Manager. This could problem could be malware or non-malware related. For example, there are worms like W32/Lovgate-AD that will cause the same problem you are experiencing. In addition to other files it drops iexplore.exe in C:\Windows\system32. The legit iexplore.exe is located in the C:\Program Files\Internet Explorer folder.
For others the problem was related to the Yahoo toolbar and uninstalling it was the correct solution. Prior to doing this all anti-virus and anti-malware scans found nothing suspicious.
Another possible cause has been traced to instant email notification settings at various board forums. A new instance of iexplore.exe was created each time the user opened an email, clicked a link and visted a forum. They were also using Spyware Doctor and the problem only occurred if that program was actively running in the background. When Spyware Doctor was disabled, the problem did not occur.