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I have been working on this problem for 2 days and I finaly solved it! I have been trying everything, like the tips above but nothing worked!
My problem was that my inbox was not syncing at all with my G-mailaccount. I have 4 IMAP-accounts and 3 worked but not the 4th one, it just did not sync! The solution for me was actually not found in Outlook, it was in Gmail.
The solution for me was:
- Log in to gmail by webmail
- In Gmail click on "settings" then the "labels"-tab
- I unchecked the "system labels" that I do not us, but more important I deleted a label at the end of the page called "[Imap]/Inbox". I don't know if this label was created by me in the past or by the system, but it did not work in Outlook 2013 anyway. It seems like Outlook 2013 thought that this was my inbox, eventhough it was just an empty "folder".
Everything still worked on my old computer with Outlook 2010, even with this label, so I think the new Outlook 2013 was more sensitive to double labelnames. After deleting this label i reinstalled the mailaccount in Outlook 2013 and everything work perfect!
I hope that this saves 2 days of extra work for someone else...