I always held the general impression that using machines and being green were inherently incompatible. When it comes to the battle between dishwasher and man, my friends tend to agree: some said hand washing was definitely greener and some, one of which referenced the "heated dry" function, were torn. However, contrary to popular belief, manual labor, conveniently, may not be the answer.
Collin Dunn did a detailed comparison of EnergyStar dishwashers and hand washing. I've adapted some of his analysis in order to compare hand washing to conventional dishwashers. Water and energy use for hand washing was determined assuming [warm] water use equivalent to that in a dishwasher cycle. For example, 54 dishes (the typical capacity of a dishwasher) washed in 6 gallons of water (the typical amount of water consumed in a dishwasher) means that only 1.75 cups of water from the faucet can be used per dish. If fewer dishes need to be washed, say 27 dishes, then the equivalent water use would be 3.7 cups per dish.
These numbers may seem confusing. Reference Dunn's article for more detailed calculations.
Moral of the story? When you have a large number of dishes piled up, go for the dishwasher. It's usually more efficient in terms of water use. Because energy use is heavily dependent on your type of dishwasher and water heater, comparing the two is a crapshoot. If you turn off heated dry, the odds will probably strongly favor dishwashers. If you only have a few dishes and can't wait to fill up the dishwasher, hand wash them. Below are some ways you can make each method more efficient.
For dishwasher tips, go here. To learn more handwashing tips, try this site. Also, learn why pre-rinsing is bad.
There are also a bunch of studies that back up these findings (and may favor dishwashers even more). Here are a few: