While not strictly necessary, turning off your fridge has a couple of benefits. Keeping the door open will let the cold air out and your fridge will run a lot if still turned on, wasting electricity (and probably making you more uncomfortable with cold fridge air).
There is also a slight risk of having the appliance plugged in while using liquid cleaning solutions or around melting ice. In general, however, the electrocution risk is less than that of wrestling the appliance out of its spot if you need to reach the plug. Use your best judgment.