What determines color -- wavelength or frequency? What determines the color of light -- is it the wavelength of the light or the frequency?
(i.e. If you put light through a medium other than air, in order to keep its color the same, which one would you need to keep constant: the wavelength or the frequency?)
 A: Refraction experiments show it is the frequency that determines color. When a beam of light crosses the boundary between two medium whose refraction index are $(n_1,n_2)$, its speed changes $(v_1=\frac{c}{n_1}; v_2=\frac{c}{n_2})$, its frequency does not change because it is fixed by the emitter, so its wavelength changes: $\lambda_1=\frac{v_1}{f};\lambda_2=\frac{v_2}{f}$.
 Now, it is an experimental fact that refraction does not affect color, so one can conclude that color is frequency dependant.
A: Here's my addition. Many of the answers above use the erroneous argument that frequency is the determining quantity, on the basis that the same object viewed in different media appears to be the same colour.
This is meaningless, since the light has to travel through the vitreous humor (with refractive index 1.33) immediately prior to reaching the retina. Thus light of a given frequency will also reach the retina with exactly the same wavelength whatever medium that light has travelled through to get there.
No: the answer must be based on the physiology of the receptors. However, I do offer one obvious experiment in favour of frequency rather than wavelength. During a vitrectomy, the vitreous humor is temporarily replaced with other substances, often air or other gases with a completely different refractive index. In none of the few articles I have read, often for the patient's benefit (e.g. here) does it mention drastic changes in colour perception as one of the temporary side effects.
Therefore I deduce that since the frequency of the light is invariant, but its wavelength as it reaches the retina could be changed by 30%, that it must be frequency that determines colour perception.
A: TL;DR: The frequency of a light wave does not change from medium to medium while the speed of light (and thus wavelength) does. By knowing the frequency of an EM wave you know it's color in any medium. 

Building on prior answers, the facts are: Color is determined by the energy of the EM Wave that reaches your eyeball. Energy is defined as $E = hf$, where $h$ is Planck's constant and $f$ is the light's frequency.
Thus, the color of an EM Wave is defined by its frequency.
In other words, measuring the frequency of an EM Wave is sufficient to identifying the color of light or the type of EM Wave that it is. This is opposed to measuring the wavelength, which would knowledge of what the refractive index of the medium that the wavelength was measured in is to determine what color of light or type of EM wave the EM wave is.
Note:
Although $f$ can be defined by $v/l$, where $v$ is the speed of an EM wave in a medium and $l$ is the the wavelength in a medium, upon changing mediums the only constant is the frequency of the wave. 
An example of why frequency is the defining factor:
When you throw a red brick in a pool, the wavelength of the EM Wave carrying the color of the object varries. If you were to measure the wavelength carrying the color of the brick, that information would be useless or misleading in identifying the color of the brick unless you knew the refractive index of (speed of EM Waves in) the medium that you were measuring in.
On the other hand - measuring the frequency of the EM Wave carrying the color of the brick anywhere would be sufficient in determining the color of the brick is Red, for it does not change regardless of what medium the EM Wave is found in.
From this, we can conclude that the color we see is dependent on the frequency of the EM Wave. (The Wave just happens to have an certain wavelength at that speed of EM wave determined by the medium the wave is in.)
A: Colour is defined by the eye, and only indirectly from physical properties like wavelength and frequency. Since this interaction happens in a medium of fixed index of refraction (the vitreous humour of your eye), the frequency/wavelength relation inside your eye is fixed. 
Outside your eye, the frequency stays constant, and the wavelength changes according to the medium, so I would say the frequency is what counts more. This explains why objects' colour don't change when we look at them under (transparent) water ($n=1.33$) or in air ($n=1$).
A: For almost all detectors, it is actually the energy of the photon that is the attribute that is detected and the energy is not changed by a refractive medium. So the "color" is unchanged by the medium...
A: Actually, there is something important all these answers are missing. Color is determined by the response of the human eye, not by energy or frequency. In order to get the full range ('gamut') of colors, I need a mix of red, green and blue light (hence the RGB displays) and the primaries can themselves all be different frequencies. That is, one RGB system can have one frequency for the red, while another has a somewhat different frequency for red, the only hard and fast requirement being that both of them choose that frequency from somewhere in the red range. But the choice affects the gamut.
Now I said "human eye", but of course, other animals see colors, too. Bees see colors into the ultraviolet. But of course, we have no idea what the ultraviolet colors look like to them, only that they do see them, and can distinguish shades of them.
Wikipedia has a lot of good further info on this, but it is scattered among several articles. Probably http://en.wikipedia.org/wiki/Color_theory#Color_abstractions is the best starting point. For something much more thorough and technical, see Poynton's excellent Color FAQ at http://www.poynton.com/ColorFAQ.html
A: As FrankH said, it's actually energy that determines color. The reason, in summary, is that color is a psychological phenomenon that the brain constructs based on the signals it receives from cone cells on the eye's retina. Those signals, in turn, are generated when photons interact with proteins called photopsins. The proteins have different energy levels corresponding to different configurations, and when a photon interacts with a photopsin, it is the photon's energy that determines what transition between energy levels takes place, and thus the strength of the electrical signal gets sent to the brain.
Side note: I posted a pretty detailed but underappreciated (at least, I thought so) answer to a very similar question on reddit a few days ago. I could edit it in here if you find it useful.
A: Light goes through your eyeball (much larger than the nano-meter scale wavelengths of visible light) before it hits the retina.
$$ \lambda f = v = \frac{c}{n} $$
Where $\lambda$ is the wavelength, $f$ is the frequency, $v$ is the velocity of the light, $c$ is the speed of light in a vacuum and $n$ is the index of refraction. Since both $c$ and $n$ are constants there is a fixed frequency for any given wavelength. The energy of an incident photon is also fixed, according to Planck's equation: $E=hf$ where $E$ is energy and $h$ is Planck's constant.
In this case, a measurement of $E$, $\lambda$ or $f$ is a measurement of all three.
A: Light frequency and wavelength are inversely proportional with a constant that is the speed of light (constant in vacuum). Both describe basically the same color within the spectrum, when light traverses a medium with a refractive index, its speed changes and affects the ratio of frequency to wavelength. What really matters is the energy carried by light as it hits the eye retina and its light sensing nerve cells.  These cells get stimulated with a certain strength and that creates a stimulus which propagate to the brain for interpretation of color scheme. Further interpretation of wavelength to frequency relation will have to incorporate the special relativity where an observer is with the light of outside and/or the quantum interpretation of wave as particle of wavelength.  But truly all of these are only but interpretations while the true knowledge is defined in absolutism.  The true statement can be stated as "there is only the Atom and everything else if opinion" or in a more precise form "there is only God and everything else if opinion"...
A: In my opinion both because frequency determines the main category of EM radiation such as: Radio waves, Microwaves, Infrared etc... Inside each category you can access a precise range of wavelenght. So colors are all the combination of frequency in the range 428 THz – 749 THz and wavelenght in the range 700 nm – 400 nm.
A: I think it is wavelength. But then wavelength and frequency are related. Longer waves have smaller frequency and vice versa.
As suggested - color is a human (or animal) construct with no specific meaning to light wave (EM radiation)
