What will cause air condition unit to stay on long periods of time and freeze up and not turn off ?

It could be your thermostat. If it's a newer programmable model change the batteries. You may have to reset or replace the whole unit as well; at least they are fairly inexpensive these days. Another possibility is the thermostat wire is shorted; this could happen if there has been any work done throughout the house. One last option is the contactor on the outside condenser is stuck. This is a mechanical switch that is thrown when the unit turns on and it should disconnect when the unit shuts off. The power to the AC unit should be shut off before inspecting this or anything else inside the condenser Very Important.

If you have any other problems with your system you can check this site for air conditioning service help.