Some people respond poorly in emergencies. The fight-or-flight response causes their brains to lock up and they freak out, instead of making rational decisions. They'll burn out the breaks trying to break normally, for example, or just do nothing until they run into something. Even though in such a situation any combination of fully breaking, shutting off the engine, picking the accelerator pedal up with the edge of your shoe, using the emergency brake, or shifting into neutral would probably be more than sufficient.
Thing is, just jamming on the brakes will stop your car, every time. Your brakes are much more powerful than your accelerator. The problem is when a driver thinks their foot is on the brake, when it is actually on the accelerator. So mashing their foot to the ground just exacerbates (i.e. causes in the first place) the problem.
Indeed, that was the first thing I listed. In an emergency you should condition yourself to jam on the brakes. That will stop the car, even if the accelerator is running.
However, some people will try to apply the brakes gradually (as you would when coming to a stop normally). And in that case the brakes won't respond as one might expect. If the brakes don't seem to work, push harder until they do.
Also, if you use your brakes to slow down with a stuck accelerator but not stop you can wear out your break pads fairly quickly at 60 mph. At which point you're SOL.
EDIT: Reading a comment farther down, I'm reminded that this is a matter of the copper pads getting too hot rather than wearing away. Same effect though.
