Someone on a crane captured this stunning video of a full circle rainbow. Unfortunately most of us never get a chance to see circle rainbows because the ground interrupts. Here's an explanation from Phil "Bad Astronomy" Plait in Slate:
…To see a rainbow, you face away from the Sun (180°), then look about 42° away from that point (180°–138°). The drops in an arc along that angle will then bend the light back toward you, and you get a rainbow, with the colors spread out a bit because they bend by different amounts.
Oh, wait. Did I say "arc"? Because technically, any raindrop 42° away from the anti-solar point (ooh, fancy science-speak again) will bend the light back to you. We see rainbows in the sky because in general the ground is close to you. When we look up toward the sky we see for a long way, and there are lots of raindrops along your eyeline that can add their light together to make the rainbow. When you look down, the ground gets in the way, there aren't as many drops, and you don't see a rainbow.
(image above via WoahDude)