When I was younger I always wondered this myself, it was really only with the dawn of the internet that I actually looked it up and found out why this strange effect was. Well to answer your question I decided to look it up again, just to make sure I had my facts right. Interestingly the answer was actually a little different from what I expected.

As we hopefully know from high school physics, white light, and namely sunlight is actually made up of a range of different colours of light or wavelengths. This is where the colours of the rainbow come from and also where the colour of the sky comes from. So basically there is an effect called Rayleigh scattering which causes light to scatter as it passes through the atmosphere. Because of the chemical composition of the atmosphere this scattering primarily effects the blue wavelengths of light, allowing the others to much more easily pass straight through, as what we see as direct sunlight. Because of this scattering every point in the sky which the light hits effectively emits a blue light in all directions. This accumulates through the thick atmosphere giving off this very vivid blue light that the sky seems to be painted with.
(my old explanation was that because blue light has a smaller wavelength it is effected by refraction much more than the other colours, causing this scattering. This new explanation, although a little harder to understand, makes more sense.)

It is because of the filtering of the Sun's white light through our atmospere. Which contains many gases and pollutants.

It has something to do with pigment. The core of the answer can be found by looking into the relative distance of the pigments to the viewer. In the sky the pigment partials are at various distances to the viewer. This appears as blue color. The same pigments if all at the same distance from the viewer, would appear darker and a different color.