How to find good looking font color if background color is known?

If you need an algorithm, try this: Convert the color from RGB space to HSV space (Hue, Saturation, Value). If your UI framework can't do it, check this article: http://en.wikipedia.org/wiki/HSL_and_HSV#Conversion_from_RGB_to_HSL_or_HSV

Hue is in [0,360). To find the "opposite" color (think colorwheel), just add 180 degrees:

h = (h + 180) % 360;

For saturation and value, invert them:

l = 1.0 - l;
v = 1.0 - v;

Convert back to RGB. This should always give you a high contrast even though most combinations will look ugly.

If you want to avoid the "ugly" part, build a table with several "good" combinations, find the one with the least difference

def q(x):
    return x*x
def diff(col1, col2):
    return math.sqrt(q(col1.r-col2.r) + q(col1.g-col2.g) + q(col1.b-col2.b))

and use that.

This is an interesting question, but I don't think this is actually possible. Whether or not two colors "fit" as background and foreground colors is dependent upon display technology and physiological characteristics of human vision, but most importantly on upon personal tastes shaped by experience. A quick run through MySpace shows pretty clearly that not all human beings perceive colors in the same way. I don't think this is a problem that can be solved algorithmically, although there may be a huge database somewhere of acceptable matching colors.

Similar to @Aaron Digulla's suggestion except that I would suggest a graphics design tool, select the base color, in your case the background color, then adjust the Hue, Saturation and Value. Using this you can create color swatches very easily. Paint.Net is free and I use it all the time for this and also the pay-for-tools will also do this.