There are two types of decapitation, one can be survived, one not. Medical decapitation is just the separation of the spine from the head, which is very painful, and will most likely result in death, but has been treated successfully.
The other type, the one you are thinking of, is a funny circumstance. Scientific evidence gathered in the French Revolution, where else, found that the head survives for a surprisingly long period of time. They were known to show expressions of fear, surprise, anger, and, on one memorable occasion, try to speak. (The story goes that the researcher grabbed the head an said "Did it hurt?" The answer was "Yes.") Recent accounts have the head living for as long as thirty seconds in certain circumstances, though this is always though the testimony of people close to the cause of the trauma, meaning unreliable sources.
In old U.S.S.R experiments, a dog's head was kept alive for a substantial period, separated from its body, hooked up to IVs, you can find the video online, but this was under controlled conditions.
Anyhoo. All human decapitations ended with death, but most are alive long enough to feel the drop on the other side of the chopping block, and even mouth a few swears at the audience before popping off. This is a major reason that decapitation is no longer considered a humane way of implementing the death penalty.
