If you want the vast majority of visitors to see your web pages as they appear to you, you will have to limit your graphics and text colors to what is called the safety palette or web-safe palette.

The web-safe palette system persists as being the palette with the greatest number of distinct colors, where each color can be distinguished individually by human eyes.
From Wikipedia, the free encyclopedia

Safety Palette

A safety palette is a group of 216 colors that will display the same colors on all monitors - the colors won't dither.

What is dithering? It occurs when a computer system limited to 216 colors attempts to display an image produced in a larger palette. It doesn't have the exact color available so it simulates the color by combining the limited colors it does have..." it dithers the color".

This can produce some very strange, murky, dull colors that can ruin a graphic. Below are two examples: the first is in 16 million colors and the second is how this same graphic would display on a 216-color capable monitor. (I magnified them so you could see the difference a little better.)

Color dithering example
Example of color dithering

How important is it to stay within the safety palette range? It depends on how wide an audience you want to reach. As more and more users upgrade to newer systems, this may become less of a problem.

However, keep in mind that not everyone with 32-bit color capability chooses that monitor option. So, the decision is yours. If you feel the majority of your web site visitors will have high-end systems with full color capability, then, by all means, use a larger color palette. Use of color is a very important consideration in web site design.

Web-Safe Color Palette

Color Effects

Colors themselves can elicit different emotions:

Red and Orange - denote power and energy

Yellow - Stimulating and fun

Green - a calming effect

White - neutral but very important

Black - serious

Designing Web Pages

Designing Web Pages

Designing good webpages begins with good webpage layout. So what do you want on this most important first screen?

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All About Design Principles and Elements

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Designing your Homepage

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Writing for the Web

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9 Ways to Make Your Web Site Look Great

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Creating a Basic Web Design Template

A "template" is simply a design format which you can apply to all (or most) of the pages in your web site.