I don’t know exactly what our atmosphere is made out of, but I’ve been led to believe that whatever it is, is responsible for the sky appearing blue. What would the atmosphere need to consist of for, say, a brown sky?
What, you mean besides the normal stuff hovering above LA or any other major city? 
Considering the light is scattering due to refraction and absorption, I doubt the colors would be different. Perhaps the gradation would be different.
Scattering, refraction, and absorption are three different things.
In the visible region of the spectrum, atmospheric absorption is negligble - as long as you ignore special conditions like clouds, pollution, or the extremely long pathlengths of sunlight at sunset.
Refraction, or bending of light rays, is ignorable except at sunset and sunrise, when you can see refraction do funky things like warp the sun’s disc into funny shapes, color the clouds prettily, or make the infamous “green flash.” Generally, it’s the boundaries between atmospheric layers that bend the light
The blue coloring of the sky is due to scattering of individual photons off of individual gas molecules. There is also some scattering from aerosol particles, but they also absorb, so molecular scattering dominates the visible spectrum. Scattering is higly dependant on the wavelength of light - specifically, to the fourth power of wave number (inverse of wavelength). Thus, red light, at 700nm, is scattered about 9.4 times less than blue light, at 400 nm. So an atmosphere is always going to be more blue than red. But that doesn’t mean it will always make for a blue sky.
Scattering is also dependant on particle size. The size of a typical air molecule, either N2 or O2, is just about 1 millionth of a millimeter, or one 700th the wavelength of red light. This happens to be just enough to noticeably scatter blue light but not red. This will also be true for just about any atmosphere made up of commonly seen gases: hydrogen, CO2, methane, oxygen, nitrogen, etc., because these molecules are all approximately the same size.
Now you’ve probably seen this next part before. Because of this color-dependant scattering, much more of the red light from the sun comes directly through the atmosphere. But the blue light gets bounced around like a steel ball in a pachinko machine before it gets to your eyes, and when it gets there, it could be coming from any direction that looks through a lot of air. That’s why the sky looks blue - because the blue light from the sun followed a long, tortured path but the red (and orange and yellow etc) light came straight from the sun. It’s also why the sun looks more and more reddish as it sets, and why red is the dominant hue of sunsets.
Now let’s consider some other possible atmospheres.
Mars: Mostly CO2, with some other stuff like water vapor, nitrogen, oxygen, etc… But it’s real thin, so scattering will be weak. So clear martian sky will be a dark blue, because there’s just a bit of blue scattered light comeing at you from directions other than the sun. However, martian air is thick with suspended dust. This is real fine dust, finer than talcum powder, so fine that it floats in the air for a long time. And with this dust, reflection, diffusion, and absorbtion come into play. So when you look at a random patch of Martian sky from the ground, you’re going to see a lot of dust-scattered and dust-diffused light. And since this dust is red, it scatters and diffuses more red light than anything else. So unless it’s an unusually calm Martian day, the sky will appear reddish to some degree. You may also see rings around the sun that come from specular reflection off dust particles.
Now let’s consider a hypothetical planet, planet Smaug. Let’s say that due to some complex geochemical processes, Smaug’s sky is principally complex hydrocarbons: big messy nasty molecules that would send the EPA into conniptions if it were emitted in any kinds of quantities here in the USA. These molecules are big enough to scatter, but not as big as Martian dust. Such large molecules will make the sky appear brownish, since a significant amount of red sunlight will also be scattered along with the blue, and there will also be a noticeable coloration due to absorption, since a lot of these chemicals are not transparent over the entire visible spectrum.
Finally, as long as we’re getting hypothetical, the color of the starlight will also have an effect on the sky color. There are a lot of very red stars, that emit very little blue light. Then there are bluish stars that appear blue to us not because they don’t emit any red, but because they emit a lot more blue than other stars. The skies on planets around these stars may appear a deep blue, or even indigo.
And that gets us into the complicated area of perception - I don’t understand this fully, but in general, the color that something appears to us has a lot more to do with the colors of the things around it than with its actual color, or the color of the light that illuminates it. On some planets, this may have a significant impact on our perception of the sky color - making it possible for some planets’ skies to actually appear green, or gold, or even magenta to our eyes!
that may be the most thourough answer I’ve ever seen on this board
As bughunter said, our sky is blue because the molecules and particles in our atmosphere scatter blue light (blue/violet light has the shortest wavelength of the visible spectrum and is most susceptible to scattering because the molecules and aerosols are of the same size…longer wavelength red light rolls right over these particles).
Places with no atmosphere such as the Moon have a black sky.
Venus has a yellowish sky due to the sulfur content in the atmosphere and because it’s atmosphere is so thick that shorter wavelengths like blue get scattered back to space before reaching the ground.
Mars’ sky has some blue in it but it more of a salmon pink color due to red dust in the atmosphere.
[Sidetrack]
This is like the ‘white balance’ thing on Video cameras, which counteracts the effect of non-white lighting; look at a piece of white paper under artificial (incandescent) light and it will look white; take an ordinary photograph and it will appear yellow, likewise under flourescent light it will still look white to the human eye, but in an ordinary photograph it may look pinkish or greenish.
All that is happening here is that your brain is tricking you into seeing the thing as white because it ‘knows’ it is white and can deduce this from the effect of the tinted light on a range of familiar objects (something like that anyway).
However, if the light source is sufficiently off-white and there are no familiar objects for reference, the brain can no longer ascertain the true colour in order to trick you and all sorts of odd perceptive effects follow.
[/sidetrack]
I have always understood (2nd year Uni Astrophysics) that the blueness of the sky is largly due to the scattering effect of DUST particles in the sky rather than any effect from individual gas molecules, which would be much too small to have any effect on light photons. [/awaiting correction and/or rebuke]
[/corrects self] :o
Hmmmmmm
Gp
Further quote from this site
Gp