Hanging is a form of punishment by which an individual is suspended in the air by a rope around the neck until dead, either through strangulation or a broken neck.
On the Skagaran colony in 2153, a Human posse led by Deputy Bennings hung a Skagaran for alledgedly killing a man named Clay Stanton. (ENT: "North Star")
As part of a conviction for fraud, Deneb V offered a guilty party the choice of death sentences. One was death by hanging. (TOS: "I, Mudd")
After her crew voluntarily chose to disobey her orders in 2375, Kathryn Janeway remarked that they could all be "hanged for mutiny", a reference to the ancient naval custom of hanging mutineers. (VOY: "Night")