In
England, the
long drop was used after its invention in the early 1800's. In
France,
decapitation was much more common.
Americans had a variety of methods. The
famous slapping the
horse was only done without access to legitimate
gallows. Any
tree would do. The person to be hung was placed on the back of a horse, their
neck tied to a tree branch. Some helpful guy would then slap the back of the horse, causing it to leap forward, and the rider could obviously only follow as far as the rope, which would proceed to break his neck.
It should be noted that hanging yourself uses quite a different technique. Cp. Gallows Dance