Not usually. The oil inside the differential runs relatively cool and doesn't get very dirty, so it usually is capable of lasting the life of the differential. If your vehicle has over 100,000 miles on the odometer, however, an oil change for preventative maintenance might help your differential see another 100,000 miles.
Few differentials have drain plugs anyway, so changing the oil can be difficult. If you don't want to remove the rear cover or separate the differential housing from the axle to drain out the oil, you can insert a length of plastic tubing and use a suction pump to siphon most of it out.
If you notice any grease or wetness around the differential pinion gear seal, or at either axle seal, the seals are leaking, and the differential is probably low on lubricant. So be sure to check the oil level in the differential.
An inspection plug is usually located on the side or rear of the differential for checking the oil level inside. The level should usually be at or near the plug opening. You can insert your finger through the opening to feel for the oil level or use a short piece of wire like a dipstick. If the oil level is low, add the specified gear oil until the proper level is achieved.
Most rear-wheel drive vehicles require 75W, 80W or 90W "hypoid" gear oil. Vehicles equipped with limited-slip or "Posi-traction" differentials require a special friction-modified gear oil.