When Mikhail Svarichevsky found out he could buy liquid nitrogen locally, he quickly got his hands on some so that he could run some experiments. He was curious about how far he could push the Arduino, and he wanted to know how the cooling would affect other components.
Obviously, the idea of using liquid nitrogen to cool an Arduino for the purpose of overclocking is silly. Mikhail acknowleges this right off the bat. If performance were the goal, there are better options than an Arduino. But Mikhail had other objectives in mind. In order to properly test the limits of the Arduino, he knew he would have to create testing methods and figure out a way to actually overclock the chip in the first place. As the Arduino's clock is set by an on-board quartz crystal, which means the frequency can't be changed, he built an external clock to push the microcontroller faster.
He discovered some interesting things as he began to cool the Arduino in the liquid nitrogen, using the on-board LED and an external LCD as status indicators while running tests. First, his on-board LED changed colors due to the widening bandgap, then ultimately stopped lighting at all. He was able to reproduce this effect with an orange LED on video so you can see it.
Click over to his page for all the details, but in short he was able to roughly double the frequency after disabling the brown-out protection and further fiddling. However, his findings come at a bit of a cost: He vaporized 3 litres of liquid nitrogen for a single hour of operation.