A little something I discovered through both practice and education: If you’re overall design is colorful, don’t make the icons colorful. Rely on their form instead. Otherwise they will be hard to distinguish and the colors won’t really stand out. Plus your pages will look like a Lisa Frank nightmare. If, instead, your overall design is monotone or subdued, color can have a more important roll in the icons you use. It’s all a matter of contrast.
Though even then it depends on how many icons you use. There are only so many colors that the average human eye can easily distinguish. It’s not a great idea to have users have to tell the difference between, say, two different shades of green for two different icons if it is at all avoidable.