What causes a fridge to stop cooling

Common issues for a fridge not working are listed here:
 

No power to the unit

Check if there is power. The most common issue is that plugs are not turned on, breakers tripping or a damaged power cable.
 

Too much ice-build up

Excessive build up inside a fridge can cause it to go warm as ice is an excellent insulator. This restricts the evaporator from drawing heat out the fridge. If you notice ice build-up, turn the fridge off for a couple of hours with the doors open to melt the ice.  Read here on why a fridge builds up ice.
 

The compressor has blown

A faulty compressor usually makes a weird noise or not making a noise at all. A qualified technician will have to test this.
 

Low or no gas

If the fridge is low on gas, this means there is a leak. Before re-gassing, the fridge should be tested for leaks.
 

Thermostat set on low

Try adjusting your thermostat and see if the compressor comes on and cools the fridge down.
 

Faulty thermostats

This is more common than expected. A faulty thermostat could be the problem for a warm fridge. Test the thermostat by turning it a few times. This can sometimes clean the contact.
 

Stuck defrost cycles

Frost-free fridges use a defrost system which could be faulty. A technician will need to test this.