I was having big problems with Outlook 2011: it was taking longer and longer to launch (up to a couple of minutes), and then being generally sluggish in use.
What I initially did was this: after ensuring my email was synced with Exchange, and nothing stored locally (in 'On My Computer' folders), I used Microsoft Database Utility to create a new identity, which rebuilt my local copy of all my email. This sped things up considerably - although not as fast as I really wanted - but introduced another problem: that searching in Outlook wasn't working. This is a problem that evidently a lot of people suffer from, and the usual solution is to re-index the drive, or the Identity folder. But in my case, searching from the Spotlight icon on the Mac's menu bar was giving results (just not when searching in Outlook) so clearly the Spotlight (mdutil) part was working fine.
As a last act of desperation, after quitting Outlook I renamed the identity (which was called 'New Identity 04/04/2011') to 'Main Identity' and relaunched. BOOM! Launching took about two seconds, AND searching was working again!
So, create a new identity, rename it to 'Main Identity', and you should get a whole new, speedy Outlook.
[crarko adds: I haven't tested this one, although I recall doing similar things with Entourage, usually when the database had become large.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20110406113513693