The debate about consciousness following decapitation via the guillotine goes back to the guillotine's use during the French Revolution. A famous story concerns Charlotte Corday, who was executed in 1793 for the crime of assassinating the revolutionary Jean Paul-Marat. Marat was a well-known journalist who enjoyed a great deal of popular acclaim, and so his assassination was considered to be not only a crime but an outrage against public sentiment. When Corday was executed for the crime, therefore, the crowd wanted to see her humiliated. When she had been guillotined, the executioner picked up her head and slapped her. Witnesses reported that:
Corday's eyes turned to look at the man and her face changed to an expression of indignation.
Following this incident, actual experiments were conducted on recently guillotined individuals, in which they were spoken to, asked to blink, to try to speak, etc. It was reported many times that the eyes and lips of the decapitated heads appeared to move upon command.
Modern science, however, understands that these movements are likely only involuntary muscular reactions and contractions rather than consciously controlled movements. The loss of consciousness is probably not instantaneous, but most likely occurs within 2 to 3 seconds. The brain, separated from the spinal column, immediately begins to shut down and die. So, while it is not impossible for consciousness to continue momentarily after being guillotined, it also isn't very likely. And of course, there aren't any survivors to relate their experiences.