Why is the sky blue?

A clear cloudless daytime sky is blue because molecules in the air scatter blue light from the Sun more than they scatter red light. This scattering effect is known as Rayleigh scattering. Because the blue light is scattered in random directions, some of it reaches the planet surface, where we see it.

When we look towards the Sun at sunset, we see red and orange colors because the blue light has been scattered out (filtered) and away from our line of sight.
In the evening, the sky sometimes looks orange or red because of air pollution. dust, water vapor, and other floating particles in the air act as a filter on the sunlight. When the Sun is low, the air layer is thicker and the light is more filtered, so it looks yellow, orange and finally red.

In more detail:

Light of a particular color is characterized by its frequency and wavelenth. The higher the frequency, the more blue it appears.
Sunlight is made up of all colors that, when mixed together, produce white light. You may have seen a rainbow or the prism experiment where the white light is split up into several colors.

The earth's atmosphere is filled with minute dust and water particles that act like a filter, scattering the light rays. The rays of light with the longer wavelengths, such as reds and yellows, tend to pass more easily through the atmosphere, while the rays with the shorter wavelengths, like blues and indigos, tend to be randomly scattered more easily. These more easily dispersed shorter light rays are what give the sky its blue color.

Red skies at sunrise and sunset are caused by the same phenomenon. When the light hits the Earth at an angle it has more of the atmosphere to go through; this increases the filtering effect and that is why you see a red sky.