It honestly depends on the model of refrigerator. Anything newer then 1998 I would recommend shutting them down when not in use. The new systems by both big manufactures have issues with the boiler area of the cooling unit. They switched to a thiner walled tubing and will eventually break open the weld at the bottom of the boiler tube or just above that where the heating element tubes are welded on to the boiler. By shutting the newer refrigerators down when not in use it will prolong the lifespan of the fridge.
The pre 1998 fridges, for the most part do not have the same issues. In the case of the older fridges it is going to be a corrosion issue on the evaporator head that causes failure. This is caused from the frost that builds up on the evaporator head during operation then melts when turned off, leaving water that is trapped on the steel tubes which causes corrosion. In the case of the older model refrigerators, it is best to leave the refrigerator on as much as possible as frost on the steel is better then pools of trapped water.
As someone mentioned above, it is very critical that in all cases the refrigerator is level when stationary and in operation.
I hope this information helps.