Why does an engine keep running after it is turned off?

There are many possibilities. More information is needed. If it's a 70's era car that's dieseling, could be the timing is off, or the anti-dieseling solenoid isn't working. If the car has had an electric fan installed recently, and won't shut off when the fan is running, the fan is not properly wired. If it's a computer controlled car, could be a problem with the ignition switch or ecm.