There are a few things you can check to stop duplicate email messages.
Start by checking Rules to be sure that copies are not being made to the Inbox, and make sure that all your rules end in "Stop Processing" actions.
Then check the task manager to be sure that there is only one instace of Outlook running. Two instances of outlook.exe running can produce two messages arriving at the same time. You will need to then determine why two instances of Outlook were running in the first place.
Another thing you can do is to delete/remove ALL your e-mail accounts and recreate them. This worked for some people.
Also, if your running Outlook XP, be sure that you are at service pack 2 or later. You can tell if you need to upgrade at Microsoft Product Updates.
Finally, another person had this happen when he had two e-mail accounts set up - using two e-mail addresses, but the same POP3 incoming and same SMTP outgoing. What happened is that the second account was getting the e-mails from the POP3 server before they were actually deleted after the first account was finished. If this is the problem you can disable the receive on the second account. There is a Microsoft article explaining the problem more thoroughly at
http://support.microsoft.com/?kbid=284404.
