This morning my Macbook crashed for some reason, and after booting it back up I noticed Outlook wouldn't start. It would flash the start up logo and then go away. Frustrating!
It turns out the fix is very straight forward. Simply hold down the "Alt" key while clicking the Outlook application icon. The Microsoft Database Utility dialog will open and ask you if you want to rebuild the Outlook identity.
The process can take several minutes, depending on the size of your email account, but it did the trick in my case and Outlook is up and running.