Q:
Why is the sky bluer on top than on the horizon? A: Consider paths for two sunbeams: one along the horizon and the other from directly overhead. The overhead path encounters an air mass 1/38th of the mass along the horizon path. So, fewer particles clutter the path from on top. Sunlight beaming in gets scattered and therefore appears blue but it's less likely to get scattered again and again. That's why the sky looks bluer on top than at the horizon.
You might think that if a little bit of scattering makes the sky blue, then a whole lot of scattering makes the sky bluer. This, however, is untrue. If our atmosphere were ten times deeper, the sky would be white everywhere — even straight up. On the other hand, if the atmosphere were a tenth as deep, the sky would be black overhead and bluer toward the horizon.
Craig Bohren, Clouds in a glass of beer
D. Lynch and W. Livingston, Color and Light in Nature
(Answered April 11, 2001; updated Oct. 25, 2007)