My ac cools the house great but is not turning off outside any ideas what is wrong?

If you turn the cooling switch on the thermostat to the off position, does it stop running or does the room not get cold enough to satisfy the thermostat? If you turn the cooling switch on your thermostat to off and the outside unit sill runs, your contacts in your compressor contactor may be arched closed. Sometimes the coil in the contactor will overheat and expand to a point where it will bind the contactor and not allow the spring loaded contacts to open.