This is one of the most frequently asked questions I come across.
For me there is no doubt that black is a colour whether argued from an objective or subjective position (see http://colourware.wordpress.com/2009/07/03/does-colour-exist/).
If we take an objective position and argue that colour results from pigments or dyes in the world then we should note that black most commonly occurs with the pigment carbon black, an efficient absorber of light at most visible wavelengths. I see no categorical distinction between carbon black and other pigments (e.g. prussian blue, malachite green, titanium doixide). Those objectivists who associate colour with light and hence argue that black occurs in the absence of light and is therefore not a colour, can be countered with my observation that in over 25 years I have never seen an object that absorbs all of the light that falls upon it; though it is my understanding that no light ‘escapes’ from black holes. But I have seen lots of black things. In fact, most black objects reflect at least 5% of the light that falls upon them. If you look at an old CRT screen turned off the screen would look grey (not black). However, when turned on, black objects in the CRT image would look far blacker than the screen when it was turned off though they obviously cannot be emitting less light. The enhanced black is caused, of course, by contrast. Modern LCD screens are less prone to this effect and I believe this is the result of more sophisticated coatings that mean that the screen reflects less of the ambient illumination. For a nice example of contrast, see the image below; the four small grey rectangles are all physically the same but appear to be lighter as we move from right to left.
This leads us to the subjective view of colour. Colour is a perception. In this sense I see no reason to distinguish between black, white, grey, red and blue. That is not to say that there are no differences between these colours. White, black and grey are, as we know, achromatic whereas red and blue are chromatic colours of a specific hue. To argue that black is not a colour in this sense, however, would lead one to question whether white and grey are colours. Of course, some people take this position. There is a tradition in visual neuroscience to separate so-called colour processing from lightness processing in the visual system because they are believed to result from distinct neurophysiological processes. However, a modern understanding of colour perception is that colour is a three-dimensional percept; the dimensions being hue, colourfulness and brightness. I would therefore argue that black is not the absence of light since black often (in fact, usually) occurs when light is being reflected or emitted; however, black is an achromatic colour like white and grey.