h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

everyone knows that rainbows are made from scattered light from raindrops in the atmosphere, but why do the rays organise themselves into arcs and bands instead of just a random mush?

There is a guide entry on Rainbows at http://www.h2g2.com/A155837 and a little more direct reply to your query at http://www.howstuffworks.com/question41.htm

Basically, the raindrops act as a prism and the different colors refract at slightly different degrees, which causes them to separate into bands. You see it as an arc, because your eye is part of the equation, so the slightly different angles of the different colors form an arc in relation to the position of the sun and your eye.

All the raindrops put together form a consistent enough whole to act as a prism.