Running a full load of dishes in a dishwasher should save water over washing the same dishes by hand. A typical dishwasher uses between 8 and 15 gallons per load of dishes with an average of about 9.3 gallons per load (Mayer, et. al. 1999).
Some manufacturers do offer high-efficiency dishwasher models. These dishwashers use less water and more significantly, less energy than the standard models. A high-efficiency dishwasher can wash a load of dishes using 5 to 7 gallons of water.
A family that replaces a 12-gallon per load machine with a 6-gallon per load machine, and runs their dishwasher 4 times per week will save about 1,250 gallons of water per year.