Why did my car start smoking while driving then stop?

Is it white billowy smoke- steam, blown headgasket letting coolant mix with hot oil, hot enough to vaporize the water and send it out your tailpipe. this will foul the plugs so bad that it won't run, no spark plugs means no combustion and no go. Latte like goo on the inside of the oil cap is another telltale of a blown headgasket. as a desperate measure you can take out the plugs and checkthem out. if they are all gummed up at the electrode. you can try a little sanding or filling in the spark plug gaps putting them back in and trying to start it. or new plugs to sacrafice until you can fix it.

Is it black smoke? your piston rings are worn out, letting oil into the ignition chambers and that blows out your tailpipe. this usually clogs up your catalytic converter- part of the exhaust system- stopping combustion by depriving the fire of oxygen. you shouldn't knock the guts out of the Cat, it's poisonious (wear a mask) but it will get you going in a pinch