Now more associated with terrorism, it was once the preferred form of execution for the one under the ax.
Though historically decapitation was essentially a means to an end, the beheading element itself carried a powerful message, and continues to do so today. There are far cleaner and less gruesome ways to kill a person, but few things make a greater impression on the public than seeing a severed head. That shock value is used to strike fear in enemies and ensure obedience.