How Dangerous Is Liquid Nitrogen?

A British teenager has had emergency surgery to remove her stomach after drinking a cocktail containing liquid nitrogen. Liquid nitrogen is used for a variety of things, such as a coolant for computers, in medicine to remove unwanted skin, warts and per-cancerous cells, and in cryogenics, where scientists study the effect of very cold temperatures on materials.

It has also become increasingly common at top restaurants as a method for instantly freezing food and drinks, or creating an impressive cloud of vapor or fog when exposed to air.
How dangerous is liquid nitrogen?