Why Do Stars Twinkle?

image credit: Robert Hensley cc
Did you know you can distinguish between stars and planets in the sky? Stars twinkle, planets don't. Okay, that's not actually correct. The stars, planets, even the sun and moon twinkle, all in varying amounts. Anything outside the atmosphere is going to twinkle.
If you're feeling a little silly using the word twinkle over and over again, we can also use the scientific term: astronomical scintillation. So why do stars twinkle, while planets don't?