From the wikipedia article:

In addition the oxygen in the Earth's atmosphere absorbs wavelengths at the edge of the ultra-violet region of the spectrum. The resulting color, which appears like a pale blue, actually is a mixture of all the scattered colors, mainly blue and green.

and

The reddening of sunlight is intensified when the sun is near the horizon, because the volume of air through which sunlight must pass is significantly greater than when the sun is high in the sky. The Rayleigh scattering effect is thus increased, removing virtually all blue light from the direct path to the observer. The remaining unscattered light is mostly of a longer wavelength, and therefore appears to be orange.

Note that I am only considering scattering by a uniform atmosphere neglecting the effects of aerosols and water vapor. Foris's answer takes up this topic (and you can easily observe the difference in how the sky looks on a very dry day vs a very humid day).