My home heat pump compressor stop spinning.  The pump is controlled for air conditioning and heat from a central thermostat in the house.  The fan works OK and you can hear a click sound at the heat pump when the thermostat is turned on.  The house and system circuit breakers (fuses) are on.
 What could be causing this problem?

Likely the compressor motor is burned out. $$$$$$$$$$ One last straw to grasp at. There is a relay at the compressor. It is what your hear clicking. It has a coil that pulls contacts together. It has 6 terminals, 2 line in, 2 line out direct to the compressor, and smaller wires to the coil. Use a test light or meter to make sure you have power to the compressor motor with the unit (fan running) turned on. If not, work your way back to the main box looking for where the power stops. It is a 230V circuit, so both wires must be hot.