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.

Examples:

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.

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 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.

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Find the answers to grammatical puzzles like this in The Grammar Cookbook!