Shut-off valves for washing machines are connected to the end of both the hot and cold copper supply lines (pipes), usually located behind the machine. They are tightened to the pipe with a compression nut, and a water supply hose to the faucet is connected to the top of the shut-off valve with a small nut. Both this nut, and the compression nut, are the usual culprits if the valve leaks. However, the problem can be alleviated by tightening both nuts.
Place an adjustable wrench around the body of the shut-off valve. Then place a second wrench around the compression nut. This is found on the bottom of the valve, surrounding the copper pipe.
Hold the wrench around the valve body while tightening the compression nut in 1/8 turns. If the nut is fully tight but the leak continues, the supply hose nut will also have to be tightened.
Hold the wrench around the valve body and place the second wrench around the supply hose nut. Tighten this nut--again in 1/8 turns--until the leaks stops.
Never try to over-tighten either nuts, as the treads can sheer off. Only tighten them to the extent where the leak stops.