Older ones could use a ton - 15, 20 gallons, more than most people would use to do it by hand. Newer ones that comply with Energy Star use less, as gotpasswords already noted. Some high-end and European models use even less - I believe my Bosch uses about 3 gallons per full load.
The tradeoff is time - with only a small amount of water, it takes longer to get the cleaning and rinsing operations done. With a good, high-efficiency dishwasher, though, most households will save energy over hand-washing. It is important to use the machine right - mainly, run only full loads. This can be a problem for small households. With only a few dishes per meal, especially if any have baked-on gunk that will harden into difficult washability, you’re probably better off hand-washing each load using an efficient process. By the time you thoroughly pre-rinse items so they can take a long stack time (days to accumulate a full load), you’re losing both convenience and energy savings.