I have central air - every summer when I switch from heat to cool the ac runs contiuously , the temp in the house drops but the ac will not shut off. We have changed the thermostat several times. This time changing the thermostat did not help. What could it be.

If you have changed thermostat, and doesn't shutt off:
1) Another bad thermostat
2) Thermostat/Control wiring
3) Welded contacts on relay or contactor
4) House not getting cool enough?

Idetify wire locations on thermostat(colors)
Disconnecting wires at thermostat shut down AC? Then, thermostat wiring, or thermostat.