The problem seems to be caused by two updates from Microsoft; KB2837618 and KB2837643.
There is a simple solution though:
- Right click on the affected account in the left pane and select IMAP Folders
- Below the list of folders, uncheck the box for “When displaying hierarchy in Outlook, show only the subscribed folders.“
- Exit Outlook 2013 / Office 365 and restart it
- At the next synchronization the folders and mail will (hopefully) be visible