Powering down a typical computer saves around 100 Watts, depending on the age and configuration.    Turning a computer off overnight for 12 hours saves around 1.2 kilowatt hours (100 Watts x 12 hours = 1,200 Watt-hours, or 1.2 kilowatt hours). 

It might not sound like much, but when multiplied by thousands of computers across campus, 365 days in a year, it can add up to be a significant energy savings.  EPA estimates that proper power management on a computer can save up to $75 per year.    

Common myths about shutting down computers, and the facts:

Myth:  I need to keep my computer running overnight to receive important updates

Fact: Not true!  Information Technology Systems and Services staff at UMD confirmed that computers do not need to be kept on at night for updates or any reason.  

Myth:  I need to keep my computer running overnight to save its hardware. It's bad to turn my computer on and off frequently.

Fact:  Modern computers are designed to handle 40,000 on-off cycles before failure, and you're not likely to approach that number during the average computer's five- to seven-year life span. In fact, IBM and Hewlett Packard encourage their own employees to turn off idle computers, and some studies indicate it would require on-off cycling every five minutes to harm a hard drive. 

Source: Rocky Mountain Institute Home Energy Brief #7 Computers and Peripherals.

Myth: Screen savers help my computer, and prevent images from being burned onto the screen.

Fact:  Screen savers were originally developed to prevent the permanent etching of patterns on older monochrome monitors. Modern display screens do not suffer as much from this problem, so ditch your screensaver and enable power-management settings!  Some graphics-intensive screen savers actually burn twice as much energy, and can prevent the computer from entering sleep mode.

Source:  http://www.energystar.gov/index.cfm?c=power_mgt.pr_power_mgt_faq