Short answer, no.
First of all, I would distinguish at least three parts: the interpretation of color by the brain, how can we assign a color to light and how that light is emmited by objects. I'll briefly comment the first one and concentrate on the rest.
Color interpretation clearly depends on the observer: I don't even know whether we see the same colors, some animals have more primary colors and other spectrum range, etc. The rest of the answers explain this quite well.
Let's go to the physical aspects and some common misconceptions:
Color is usually associated to a particular wavelength of light, (it would be more correct to say frecuency because it's what the eye detects), but this is not completely accurate:
Magenta, for instance, doesn't correspond to any wavelength. This is because we detect color magenta when both green and violet are "mixed" in the eye.
Black color is the absence of visible light, so it's also a color without a frecuency.
Moreover, color doesn't depend only on the wavelength but on intensity too. Orange-yellow at low intensities will be detected as brown.
If we consider how "colored" light is emmited by an object before it reaches our eyes there are several possible ways.
When they don't emmit light by themselves:
Since color also depends on what light you illuminate the object with, we can't say that X has color Y unless we say how we iluminate it. It's a convention to use white light (blackbodyt at 6500K). But light's intensity is not specified, although it's modifies the color we see (if you use too much light you'll see it completely white).
It's important to say that not always an object absorb some frecuencies and reflect others. There is an important phenomenom, iridiscence which is a combination of interference and diffraction. In this case the color depends on the angle (like CD's and butterfly wings).
Opaque materials may reflect light in the same angle it hits, it is the case of mirrors. Since "perfect" mirrors reflects all frecuencies, so a mirror is white (because we are using white light).
We could say that "perfect" transparent materials have no color at all or that they are white. But in most cases there is some color due to scattering and partial reflection, which causes interference. This will also depend on how much material we have, small volume of air is colorless but the atmosphere is blue.
When they emmit light by themselves:
This depends on the temperature (blackbody radiation), chemical reactions, electric currents, etc. So in this cases color will also depend on time.
Other problems would arise for single particles, like electrons (we could associate some color using Compton's scattering)...
There are many more subtleties, but I'd say we can conclude that color is not a fundamental property of objects, only an useful characteristic in some cases.
Note: I think I use too many parentheses.