Why are color values stored as Red, Green, Blue? I learned in elementary school that you could get green by mixing blue with yellow. 
However with LEDs, TFTs, etc. you always have RGB (red, green, blue) values?
Why is that? From what you learned in elementary yellow would be the 'natural' choice instead of green. 
 A: When you mix colors using Watercolors, then they mix as "Subtractive Colors". However, Light itself mixes as "Additive Colors". 
Even though it might seem strange why the inherently same thing works so differently, it makes sense if you think about Watercolors, etc. as absorbing everything but that specific color.
A: What @Michael said, plus your retina has sensors for roughly red, roughly green, and roughly blue, and not for any other colors.
(BTW, the green sensors are more sensitive, so it takes less green to make the same brightness.)
When you see something yellow, it's in between red and green, so it excites both of them, and your visual cortex happens to call that combination yellow.
If your TV set turns on a red and a green pixel so close together that you can't tell they are separate, what does your brain call it? Yellow, because there's no way it can tell the difference between real yellow and red plus green.
Paints work by subtracting colors, not by adding them.
Blue subtracts red and green, and yellow subtracts blue.
When you mix blue and yellow paint, the color that is least-subtracted is green.
Colors you get by mixing paints tend to be muddy, as opposed to brilliant.
A: The inherent difference is things that emit colors, e.g. LEDs, and things that place substances on a surfaces to color them, e.g. printers. In the latter case, the CMYK (cyan, magenta, yellow, black) space is commonly used, rather than RGB, so you were on the right track with yellow. BTW, black is there because the black produced by mixing C, M, and Y doesn't look as good and printers generally print black stuff on white paper).
On a philosophical note: color is not a physical property of an object, i.e. we should not really talk about a "blue car"; it is an example of conscious experiences known as qualia.
A: Because these 3 colors are the only ones that the human eye can see. We have 3 kinds of cone cells in our retina, each one reacts to a specific wavelength.
http://en.wikipedia.org/wiki/Cone_cell
As you can see in this article, it happens that these three wavelengths correspond approximately to red, green and blue.
Since our eye cannot see more than 3 wavelengths, you don't add a lot of information if you add a fourth color. 3 seems like a good tradeoff between space needed to store a picture and fidelity.
I our eyes had more types of cones (like cones sensitive to infrared or ultra violet) we would certainly use more colors to encode our images.
