This is partly down to a feature of the video system called "gamma", which is a measure of how the binary data is translated to screen brightness. Macs and PCs are different.
It can also help if your monitor is properly adjusted. The Brightness control should be used to set the black point, so that an image black is only _just_ distinguishable from the screen. Then Contrast is adjusted to set the white point.
For Windows PCs, there are all sorts of utilities to help, some supplied with video cards. If there is something that can with your video card, use it. Otherwise, I can recommend a program called Quickgamma for a basic setup.
The Net Safe colours are a standard set, which can be supported on a
256-colour system without any messy dithering. This is not quite the same as them being nice colours, but they're worth sticking to.Under various disability laws, some colour combinations may even be illegal. Consider how a red/green scheme might look to somebody who is colour-blind.