The cause of this phenomenon depends on the type of email account involved.
In the case of IMAP accounts, Outlook 2010 and Outlook 2013 save a sent message in the IMAP account's Sent message folder and your IMAP mail provider may also save a copy. The result is two messages in the Sent Items folder every time you send a message. This seems to be most common with Gmail accounts but other IMAP accounts may be affected as well.
Change the IMAP Account's Sent Options
First, check your settings for saving Sent items. Open Account Settings (it's on the File menu in Outlook 2010 and 2013). Double click on your IMAP account then click More Settings and look at the settings on the Sent Items tab in Outlook 2010. In Outlook 2013, its on the Advanced tab.
Choose the option for Do not save copies of sent items and send a test message to see if the problem persists.
Change Outlook's Global Options
If you have only one email account in your profile, you could use the option to not save sent messages. This is in File, Options, Mail, in the "Save messages" section, uncheck the option to Save copies of messages in the Sent folder. Note that this setting will apply to all accounts - if you have more than one email account configured, you will not save sent items for any account.
For this reason, you need to be careful using the global setting in File, Options as not all mail servers will save a sent item for you when sending. It's better to disable the option to save sent items on the More Settings, Sent folder tab.
If you have an Outlook.com account, one thing that is reported to cause duplicates in MSN (and possibly other accounts) is the option to Save sent items in the folder with the original. This is on File, Options, Mail, in the Save messages section.
