What would cause a car to intermittently shutter when starting and run but then stall later when idling?

Fuel filter was replaced less than a year ago. Battery is original, factory. Car ('02 Saturn SL1) has about 125,000 miles on it. Problem is intermittent and usually occurs after car has been running and is turned off and back on. One final note: The car will turn over, run, all electrical works, no dimming of headlights. Car can be driven but will stall when idling later. Quick fix seems to be simply turning the car off then back on immediately.