tl;dr version: You want zero sharpness for computer images.
The sharpness setting on monitors and TVs is an optical illusion created by unsharp masking. It exaggerates the contrast on edges by making the dark side of the edge a little darker, and the light side of the edge a little lighter.
http://en.wikipedia.org/wiki/Unsharp_masking
Your brain interprets that increased contrast at sharpness, even though all you've done is distort the image so it's no longer true to the original image. That is, the image
looks sharper, but actually contains
less information than the original unsharpened image.
Since it's an illusion, the recommended setting for computer screens is zero sharpness. Because of the way unsharp masking works, it is impossible to make black text on a white background appear sharper using it since you can't make the black any blacker, nor the white any whiter. If the sharpness setting is making that type of text appear sharper on your monitor, then that suggests you're running at a different resolution than your screen, a problem with your video cable, or a monitor pixel alignment problem.
Check to make sure your Windows display resolution matches your monitor resolution. Try running the ClearType adjustment (control panel -> Display -> Adjust Cleartype). If you're using a VGA cable, try hitting the auto-adjust option to try to better sync the analog signal. If you're on a Mac, there's nothing you can do. Apple doesn't let you adjust the amount of anti-aliasing, in order to keep kerning (letter spacing) accurate for publishers using Macs.
On TV images, some sharpness is recommended because the image has been resized to fit the TV's resolution. Even if you're playing 1080p content on a 1080p screen, the image is resized because all TVs overscan (enlarge the image so it's slightly larger than the screen, and crop the edges). This resizing slightly blurs the image, so some unsharp masking is recommended to restore the appearance of sharpness. But computer images are supposed to be an exact match for the monitor resolution, so no sharpening is needed.