Is black a color or absence of color? When there is no light, everything is black, so how can we say that black is a color?
Black is the absense of color, which our brain visualizes to us in some way. I can't really say that I know how you percieve black. But it IS a fact that when no photons reach the photoreceptor cells in your eye, your brain will get a distinct value from it, and that value will be different than when it receives red or blue or any other wavelength of light.
The value that your brain reads from your photoreceptor cell will be different for black than for blue - but it DOES get a value. I guess that value would be 0, but it might just as well be 1 or 42 - who knows? :-) So in that sense, I would say that black is indeed a color.
In physics, it is a bit different. It makes no sense talking about colors in physics. In physics, you talk about wavelengths as a continous spectrum of wavelengths from very low frequency to very high frequency. Either there is a wavelength, or there is no wavelength.
Humans have named certain ranges of these wavelengths as colors red, green, blue, violet etcetera - because it makes it easier to communicate.
There is no range of wavelengths in the spectrum that has the name "black" - and in physics "black" means that there is no wave at all. At the same time, there is no wavelength that has the name "white", because white is a combination of all color frequencies at the same time. Our eyes give white another distinct value, in the same way as black.
No object (except perhaps black holes) are completely black. Warm objects radiate low frequency light, and can never be "black". Your photoreceptor cells might give your brain the same value as for black, for many differenct physical colors - but no objects are actually black.
So the short version of the answer is:
Your brain probably observes black the same way it observes any other color - as a certain "value" read off a photoreceptor cell - and in that sense, it is a color. In physics, nothing is black.
As already indicated by Brandon, it depends on your point of view.
If by "color" you mean the definition you find on wikipedia, then "black" is definitely a color; "black" is just how humans perceive the absence of any significant peaks in the spectrum of reflected light, and a low overall intensity compared to surrounding reflectors (or even a complete absence of light, like the night sky).
If on the other hand, you define "color" to be a particular (single) wavelength in the visible part of the EM spectrum (so NOT including any human interpretation), then "black", "white", all shades of grey in between, and a whole bunch of other things, are not colors; those colors do not appear explicitly in the spectrum (unless you define the combination of "red", "green" and "blue" to be "white", but then there is already a certain level of human interpretation).
There really is not a clear, unique and unambiguous answer to this question; whether "black" is a color or not depends on the particular set of base axioms you are using.