Hanged is used only when referring to the hanging of a person by the neck with the intention of killing him or her.
In all other cases, hung is the past tense of hang.
Correct: The murderer is going to be hanged at dawn.
Incorrect: The murderer is going to be hung at dawn.
Correct: We hung your picture on the wall.
Incorrect: We hanged your picture on the wall.
Correct: One should forgive one's enemies, but not before they are hanged.
Correct: We hung our swimsuits out to dry.
What about "Hung, drawn and quartered", then? Shouldn't it be "Hanged, drawn, and quartered"?
No, and this is why: "Hanged" is used when a person is hung by the neck with the intention of causing death. Being hung, drawn, and quartered is a rather different, very grisly, way to die: the person is not intended to die from the hanging but instead – slowly, painfully, and with a great deal of mess – by being slit open so that his guts spill out, and then chopped up into quarters.