Example:
MLB's AtBat application sometimes freezes up when watching a baseball game via MLB.tv. Restarting the app is the only fix. To do so I have to click the Home button to exit the app (because you can't use the tray to close the app you're currently in), then double-click the Home button to bring up the tray, then press & hold the app until it shakes, then 'x' it out.
It would be much quicker if there was some combination of buttons or gestures that signaled the phone to completely close the app. Such that re-entering would not bring up the saved state.