How can I define colors as variables in CSS?

CSS supports this natively with CSS Variables.

Example CSS file

:root {
    --main-color:#06c;
}

#foo {
    color: var(--main-color);
}

For a working example, please see this JSFiddle (the example shows one of the CSS selectors in the fiddle has the color hard coded to blue, the other CSS selector uses CSS variables, both original and current syntax, to set the color to blue).

Manipulating a CSS variable in JavaScript/client side

document.body.style.setProperty('--main-color',"#6c0")

Support is in all the modern browsers

Firefox 31+, Chrome 49+, Safari 9.1+, Microsoft Edge 15+ and Opera 36+ ship with native support for CSS variables.

People keep upvoting my answer, but it's a terrible solution compared to the joy of sass or less, particularly given the number of easy to use gui's for both these days. If you have any sense ignore everything I suggest below.

You could put a comment in the css before each colour in order to serve as a sort of variable, which you can change the value of using find/replace, so...

At the top of the css file

/********************* Colour reference chart****************
*************************** comment ********* colour ******** 

box background colour       bbg              #567890
box border colour           bb               #abcdef
box text colour             bt               #123456

*/

Later in the CSS file

.contentBox {background: /*bbg*/#567890; border: 2px solid /*bb*/#abcdef; color:/*bt*/#123456}

Then to, for example, change the colour scheme for the box text you do a find/replace on

/*bt*/#123456