If you're in need of a new computer, consider a laptop over a desktop. Even better, choose one with Energy Star certification. For more information, check out the Home Energy Saver site sponsored by the US Dept. of Energy.
Most laptops go into low-power mode (or sleep) when left inactive, an important feature since the majority of computers are left on 24 hours a day. (Turn off your computer when it's not in use to REALLY save energy.)
According to HES, the idea that computers should be left on at all times is a myth leftover from the days of heat-sensitive mainframes.
Image from Apple. Check out their Energy Star certified computers here.