If unplugging or turning the dial to off does not stop the water, the water valve is shot (stuck open).

If you can stop the water by unplugging or moving the dial to Off then it is probably the water level switch.

The water level switch is actually a pressure switch.
The way it works is:
There is a plastic tube that goes to the bottom of the tub.
As the water rises it builds up air pressure in this tube
When it reaches the pressure set point of the switch the switch activates.
This cuts power to the water valve (shuts the water off) and tells the machine to start agitating.

Possible causes for the level switch not working are:
1. The tube has some crud in it and will not let the water enter. Remove it from the switch and blow into it to clear the plug.
2. The tube has hairline cracks or a hole in it so cannot build up pressure
3. The tube connection at the valve is leaking. Cut off half an inch of tubing and reconnect
4. The switch diaphragm or the switch itself is shot. Get a piece of tubing with the same internal diameter as what is on the unit attach this to the switch. Start a fill. Blow into the tubing, the fill should stop. You should not have to blow very hard. If it does not stop then the switch is shot.
OR
If the tube is not blocked and is in good shape it is usually the switch.

Here is some additional info
http://www.applianceaid.com/washers.html