In theory, you could make a refrigeration system using air as the working fluid:
Compress air. Air temp increases due to adiabatic heating.
Cool air back down to room temperature.
Expand air. Air temp decreases to below room temp due to adiabatic cooling.
Use cool air for refrigeration.
Real-world systems typically use some kind of CFC/HCFC as the working fluid. The one advantage about using these compounds that I can readily see is that evaporation/condensation allows for the transfer of much greater amounts of heat energy - which means more cooling capacity without resorting to outlandish pressures/temperatures/flow rates on the hot side of the system.
Are there other properties of CFCs/HCFCs that make them well-suited for use as working fluids in refrigeration systems?