Courtesy of Wade W. Hampton: Purchase a low-power computer such as a laptop or network computer. These typically don't use as much power as desktop systems. For example, someone on the WWW had a Corel/Rebel Netwinder powered by solar cells. I find it funny that an "Energy Star" desktop still has a 300W power supply and uses far more power than a computer like the Netwinder which uses something like 10 Watts of power. Maybe there should be a new class of computers called "Energy Miser" (or similar) that use nearly an order of magnitude less power than Energy Star systems?
To save power for the display, one could purchase a LCD monitor instead of a CRT. LCD monitors consume 30-40 Watts of power versus the 100's of Watts used by most monitors. The price of an LCD is still 2-3 times that of a similar monitor, but as LCDs become more widely used, the price will come down.
Make sure that any new computer purchase includes APM-compliant hardware and low-radiation. Use TCO, DPMS or Energy Star compliant monitors.