Staring at your monitor hour after hour can cause headaches and eye fatigue. One of the easiest things you can do to help this problem is to raise the refresh rate. Monitors often come with refresh rates set too low, i.e. 60 Hz which causes flickering. A higher refresh rate helps reduce the flickering effect and lessen eye strain.
You can usually set your refresh rate under display properties/settings. Also, RefreshForce is a free tool that lets you quickly change the monitor's refresh rate.
Another cause of eye strain that many people tend to just live with is font size. Higher resolutions on monitors can cause quite small fonts. Also, many web sites use small fonts. If you catch yourself leaning toward the monitor, or squinting uncomfortably, right click on your desktop to bring up display properties, select appearance, and choose font size. You can further adjust the font you see when surfing by choosing text size from Internet Explorer's view menu and selecting your preference. This may cause some of your favorite web pages to display a little oddly, but at least you'll be able to read them!
Make sure you have proper lighting on your monitor (it's more effective to have a light shining from behind your shoulder or above the monitor than behind the desk).
Even using these measures, you should take frequent breaks from the computer. Look away from your monitor at least once every fifteen minutes; preferably, step away from the computer altogether.
Another solution is to use two monitors. This forces you to move your gaze around from applications open on one screen to applications open on the other. This can also help fight hand injuries as you'll save a few mouse clicks and keystrokes since you won't have to switch from application to application as often.