In 1905 a French doctor wanted to see how long consciousness remained in a severed head and so did a rather morbid experiment at the execution of a beheaded prisoner. The remarkable report is linked from the Wikipedia page on the guillotine.
The observations were apparently made by a Dr Beaurieux who watched the execution of a prisoner named Henri Languille and immediately tried to get the attention of the severed head to see how it would react.
Here, then, is what I was able to note immediately after the decapitation: the eyelids and lips of the guillotined man worked in irregularly rhythmic contractions for about five or six seconds. This phenomenon has been remarked by all those finding themselves in the same conditions as myself for observing what happens after the severing of the neck…
I waited for several seconds. The spasmodic movements ceased. [...] It was then that I called in a strong, sharp voice: ‘Languille!’ I saw the eyelids slowly lift up, without any spasmodic contractions – I insist advisedly on this peculiarity – but with an even movement, quite distinct and normal, such as happens in everyday life, with people awakened or torn from their thoughts.
Next Languille’s eyes very definitely fixed themselves on mine and the pupils focused themselves. I was not, then, dealing with the sort of vague dull look without any expression, that can be observed any day in dying people to whom one speaks: I was dealing with undeniably living eyes which were looking at me. After several seconds, the eyelids closed again[...].
It was at that point that I called out again and, once more, without any spasm, slowly, the eyelids lifted and undeniably living eyes fixed themselves on mine with perhaps even more penetration than the first time. Then there was a further closing of the eyelids, but now less complete. I attempted the effect of a third call; there was no further movement – and the eyes took on the glazed look which they have in the dead.
Apparently, this was also discussed in a brief article in a 1939 edition of the Journal of the American Medical Association but I can’t read it because my institution’s subscription seems to be broken (off with their heads!).
The famous French chemist Antoine Lavoisier is often said to have arranged an experiment before his execution where he would try and blink as many times as possible before his head finally died, but the story is apparently a myth.
UPDATE: Thanks to Mind Hacks reader jata for a link to the complete 1939 JAMA piece on decaptitation and consciousness which is available here.