"The Drake Equation" Helion Prime In third place: Helion Prime are a metal band who use science and sci-fi imagery the way other bands use Satanism. So this is a song about the Drake Equation. While I love the song, it only gets the bronze for two reasons: there's no video yet, and they don't actually sing the equation. With thanks to Big D of the Assorted Thoughts blog who first introduced me to Helion Prime.
In second place: Lyrics sadly became outdated as Benoit Mandelbrot passed away in 2010, but still... Here's a chalk-based animation that illustrates the song nicely, although it's a shortened version. Or if you prefer, there are about a million YouTube videos of fractal animations set to the song. Bonus points for spelling out the equation. Bonus points subsequently deducted as, obviously, the equation used in the song actually describes the Julia Set. D'oh...
"The First and Second Laws Of Thermodynamics"
Flanders and Swann
And the winner is: Flanders and Swann, those rapscallion 50s and 60s music hall entertainers. Michael and Donald were no strangers to science - songs about the mating habits of hippopotami made them the Discovery Channel of their day, while their revelations about the spiral growth of the honeysuckle (right-handed) and the bindweed (left-handed) were worthy of a PhD. Bonus points for spelling out and actually understanding the Laws, and for squeezing in the Third Law as well. There's no actual video of Flanders and Swann performing this so here's a version accompanied by random pictures and some bad jokes from teachers. Polar! Lol.