Why is the sky blue?

Because of Rayleigh scattering of solar radiation by particulate matter in the upper atmosphere!
Because of the Dilithium crystals!
Because that's the way it is!
Terrorism!

Wrong. None of the above.

"But, wait a minute! Rayleigh scattering is a well-understood phenomenon. It's exactly the reason why the sky is blue! The Rayleigh scattering cross-section is proportional to the inverse of the fourth power of the wavelength of incident light, so scattered light consists of more waves of shorter wavelengths than longer wavelengths, and since blue is near the short end of the visible spectrum, more blue light is reflected back to Earth, and so we the sky as blue!"

Yes, yes, I know how Rayleigh scattering works (sort of). Rayleigh scattering, and to a lesser extent, Mie scattering are the names we give to phenomenon that result in blue light being reflected back to Earth. They do not explain why the sky is blue. That is to say:

Nobody knows why the sky is blue.

There is no specific reason why the sky is blue, and a reason, rather than a mechanism, is what the correct answer to a question starting with "why" must be. The sky could have been orange. The OPN1LW gene, which codes for the color receptor in ?-type cone cells (which primarily detect yellow-green light, but are also solely responsible for our detection of orange and red light), could have switched places with the gene that codes for the color receptor in ?-type cone cells (which detect blue light) very early in the evolution of primates, and then we would interpret 450 nm wavelengths as 650 nm wavelengths, and the sky would be orange. Or the cis-trans conversion of rhodopsin in the retina could have occurred in such a way that made photoreception completely insensitive to chromatic variance, leaving humans incapable of even seeing color. Or I might just be making all of this stuff up.

In other words, the color of the sky might be arbitrary, for all we know.

There's a famous anecdote that Nobel-laureate and all-around-awesome-human Richard Feynman supposedly used to tell about his father from when he was younger (whether this is true, I cannot say). To paraphrase, little Feynman asked his father why, when he pushed his wagon, it kept going even when he let go of the wagon's handle. Big Feynman explained that nobody knew why this was the case, but that the name we gave to the phenomenon is "inertia," and that this was a property that everything with any mass has. We know How, but not Why. Maybe if more people were like Big Feynman, we'd have more people like Little Feynman.

So the next time a little kid asks you if why the sky is blue, or why there is lightning, or why America invaded Iraq, respond honestly: we have no clue.