The blue color of the sky is due to Rayleigh scattering. As light from the sun shines down it scatters off of (mostly) nitrogen molecules in the atmosphere. Without this process, the sky would be dark during the day except for the bright sun, moon, and stars.
Rayleigh scattering is more efficient for shorter wavelengths. So, even though the Sun provides a full spectrum, blue is scattered more efficiently than the longer wavelengths of light. Thus blue is the dominant color you see. See Rayleigh scattering (Wikipedia) for more info on Rayleigh Scattering.
So, to answer your question, the color of the sky is the same for most places on the Earth at noon because the sunlight is relatively constant and the atmosphere is relatively uniform in composition (nitrogen and oxygen). The exceptions are air pollution, high latitudes, and high altitudes. Air pollution and high latitudes have similar effects in that more attenuation of the light occurs as it travels through more atmosphere, and therefore colors change like you see at twilight. Air pollution in particular is a highly variable source of scattering and absorption that gets quite extreme when there are high concentrations of particles. High latitudes change the geometry, similar to twilight. In contrast, high altitudes have less atmosphere, so if you go high enough (e.g. in a hot-air balloon) there just won't be much scattered light and it will get dark due to the lack of atmosphere.
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.
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.