Choosing your website's color palette, despite the apparaent easiness, is one of the most difficult decisions a webmaster has to make in order to finish his/her work. The reason for this is that the color palette that will be used is very important in determining the message that the webmasters wants to come across.
I guess most psychologists agree that colors do affect the state of the mind. The human mind tends to associate a particular color to a particular emotion or situation. For example, blue brings about peace of mind while red means love or war or even both. It is vital that you play along these emotion lines and build your website's message on that principle.
In relation to this, you should use colors that are natural and not hurtful to the eyes. By natural colors, I mean light hues and hues that are not too contrasting, but remember to make a constrasting division between the background color and the color of the text. This is the single most important thing that any webmaster has to remember. The last thing that we want to have is dark blue text on a black background.
In general, most webmasters use three base colors on which the palette will be based on and use this all throughout the design. Of course you can still add some shades here and there, but the three chosen colors should be the most dominant.
If I may advise so, you should only use colors that are considered to be web-safe. These are the 256 colors that are included in a standard 256-color computer monitor. Most people still use this kind of monitor, so please be considerate. Furthermore, you should also consider people with visual disabilities in your site.
To help you decide with your pick of website colors, this article from Avangate.com has a list of reliable websites where you can test the palette you have on mind. Go ahead and visit it now.