Clothes washers use energy, most of which (typically over 90%) is for water heating. If you reduce the water temperature and the amount of water used, you will save the most energy.
If you are making a new purchase, consider a horizontal-axis washer as this design uses less water. The reason is a top-loading washer tub must be filled in order for the clothes to be kept wet. To clean the clothes, an agitator then tumbles the clothes in the water. A front-loading washer needs less water and there is no need for an agitator because the tub rotates to tumble the clothes in the water.
Washing Machine Efficiency
Before making a purchase, check the EnergyGuide labels. This label must be on all new washers. These labels will give you some idea of how much energy is used by that model washer. Keep in mind smaller models tend to show less energy use but they may not be large enough to meet your needs or cause you to have more loads to run and end up using more energy in the long run.