On occasion, Outlook 2011's database (where all of your downloaded email is stored) becomes corrupt. This usually results in Outlook becoming slower and slower over time, your losing the ability to move messages from one folder to another, or Outlook closing unexpectedly (crashing). Thankfully, the fix is a relatively simple one:

Open Outlook while holding the Option key on your keyboard. This should open the Outlook Database Utility, shown below. If this does not launch, quit Outlook and try again.

Select your primary identity, which is shown in bold (it's also typically called "Main Identity"), and click the Rebuild button. Your database should start rebuilding. This will take anywhere from 20 minutes to 2 hours, depending on how much email you have stored in that identity.

Once it's done rebuilding, click the pulsing Done button.

Done! Close the Microsoft Database Utility, and open Outlook as you would normally.