After the latest round of Office 2013 updates, some IMAP users are reporting their Inbox is not listed in their profile, is empty, or their IMAP accounts aren't syncing.
This is the result of the November 12 updates, KB2837618 and KB2837643. In addition to the IMAP problems, Outlook may crash shortly after it starts, users with Exchange 2007 mailbox may have problems setting out of office replies, retrieving free/busy or using add-ins (such as Lync) that use the SMTP address property, due to problems with autodiscover.
If the only problem is with an IMAP account, I don't recommend uninstalling these updates as they add some IMAP improvements and you'll have a better IMAP "experience" with these updates installed. If Outlook is crashing or you use Exchange 2007, you'll probably want to uninstall the update.
There are two possible fixes for IMAP accounts. The first, and preferred, method is to add Inbox to the IMAP root.
To do this, go to File, Account Settings and double click on your affected IMAP account. Click More Settings button then switch to the Advanced tab.
In the Root folder path field type Inbox. Exit the dialog and perform a send and receive. (If the Inbox is not your root folder, setting Inbox as the root won't work, as it will hide all of the other folders.)
If that doesn't work, try disabling the option to show only subscribed IMAP folders.
Right click on the IMAP Inbox folder and choose IMAP folders. At the bottom of the dialog is an checkbox for When displaying hierarchy in Outlook, show only the subscribed folders. Remove the check then close the dialog to return to Outlook. Click Send and Receive.
If the IMAP account still doesn't work, Outlook is crashing, or you connect to Exchange 2007, uninstall the update from Control Panel's Program and Features. Click on View Installed Updates, locate the update(s) and uninstall.