We keep liquid nitrogen around mainly to make ice cream with. One idle day we decided to play with it a bit. First, we thought we'd see how much harder it was to freeze alcohol than water. A friend had sold me some Everclear (95% ethanol) a few years before. I'd never touched it, and this seemed like a good occasion to crack it. What followed was the single most serendipitous liquid-nitrogen discovery we've made: if properly cooled, Everclear enters a highly viscous state in which it will pour off of a spoon like molten glass! It requires a bit of care, cooling it just the right amount while stirring constantly. If it's overcooled, it may remain in a vitrified state but it will harden so that it's uninteresting. In retrospect, it seems likely that the very rapid cooling that occurs with liquid nitrogen plays a role, since fast quenching prevents the development of large crystals in many materials. Vodka (40% ethanol) doesn't behave the same - no matter how rapidly and precisely we cooled it, it transitioned from liquid to solid with no viscous phase. The 75% ethanol psuedo-Everclear that's sold in California can be made to vitrify, but it's much more touchy; it really wants to solidify.
Other things we played with that day:
Later that year, Mike experimented with a liquid nitrogen powered rocket, with results chronicled in this icb log.
A few years later I made butane ice cubes for the Mad Science Fair.
More LN2 fun is described in ubws' 1001 things to do with Liquid Nitrogen page.