Souvenirs: One benefit of beheading is that it allows the executioners to display the victim's head as a warning. This practice dates back to ancient times, but one particularly striking semi-recent example took place in the aftermath of Nat Turner's rebellion, as posses searching for Turner allegedly killed nearby slaves nearly at random and mounted their heads on fenceposts as a warning.
How It Works: The victim is restrained, usually forced to kneel, and the executioner removes the head by way of a sword or knife. In renaissance-era Europe (most famously in the aftermath of the French Revolution), the process was automated by way of a device called a guillotine, which dropped a heavy blade through the prisoner's neck--allowing for a clean, instant decapitation.
Complications: Beheading can actually be a fairly humane form of punishment, provided that the executioner is strong and reasonably competent. When the executioner is less strong or less competent than would be desirable, however, death can be slow and excruciatingly painful.