As with most aspects of reporting and data presentation, restraint is the key when it comes to choosing colours. You may have noticed that experts in charting, such as Edward Tufte or Stephen Few, tend to choose very muted colours for the majority of their work. Bold colours are used sparingly to highlight and pick out key areas.
In Envisioning Information Tufte quotes Ann Driver to explain way, by analogy to music:
"Music without accent lacks coherence....Conversely, if every note, word or movement is stressed, the result has even less meaning."
Charts in which all the colours are bold are like speakers who shout the whole time, or music without variation. They are boring, and the key information is lost in the general clamour. On top of that, bold colours tend to clash with each other.
Choosing the colours that go is not just a job for Dulux, though, and you don't need a degree in colour theory to make sensible choices for charts. You can't go wrong, for example, with grey as a base colour and any bold colour as a highlight (red is a popular choice).
If you want to get more adventurous, my advice would be to ignore the normal RGB and CMYK colour models, which are hard to think in, and work with Hue, Saturation and Value (HSV). This gives us the very intuitive colour triangle, which I've reproduced here after the version in the excellent Color &Type.
This is a simplification of the real triangle which is a continuum from black to white (left to right), and from fully saturated at the top to desaturated at the bottom. The three highlighted axes are fertile avenues for finding pleasing colour combinations. If we choose red as our basic hue:
That gives us three options: red and grey; dark red and white; light red and black, all of which work well. Choosing a more complex colour scheme, using more than one basic hue, is harder. But the same basic principles of contrast apply—using tints and shades (in other words varying the saturation and value) will often make colours work together. Consider the notoriously difficult red and blue:
Using both colours bold is disastrous. They clash badly, making it almost impossible to look at.
By using either a tint or shade of blue we can achieve a more pleasing result, one that will make it easier to appreciate the data in a chart.
It's worth noting how warm colours such as red have a tendency to rise above cool colours such as blue, which gives the illusion that the red is "floating" above a blue background. Used with care this can be a very valuable technique to highlight key elements of a chart or slide.