1) Open up the 'Debug' perspective (while you're not running the application)
2) Click on the 'Breakpoints' tab (or open up the Breakpoints view)
3) Click on the icon that looks like J!
4) Uncheck 'Suspend on caught exceptions' and 'Suspend on uncaught exceptions'
Eclipse will only break into the debug perspective from this point on if you explicitly set a breakpoint in your code. Stack traces and log messages should display in the console as normal.