In addition to the above, it is worth noting that switching the vehicle's engine off at anything above idle speed can be very bad for the catalytic converter. In this instance, unburned fuel will enter the catalytic converter and very likely ignite on the element (the heat shield that surrounds a "cat" is there for a reason), damaging the converter and making it perish faster.
Running the engine when it is misfiring, tow or bump starting the vehicle, or running it with an over-rich air/fuel mixture will have the same effect - allowing unburned fuel to enter the catalytic converter and possibly ignite.
Moreover, running the car if it is (visibly) burning oil, or using leaded fuel will coat the element in the catalytic converter and clog its passages, reducing its converting efficiency and possibly causing an overheat.