Is the past tense of the verb "hang," hung or hanged?

Hung is both the form, and the past participle, of hang (as in hang up a telephone), so you can say:

(a) I hung up the phone.

or simply

(b) I hung up.

In this use, as in sentences (a) and (b) above, hang up is a separable phrasal verb.

Hang is also used as a transitive verb, to mean the same as hang up, as in sentences (c) to (e) below:

(c) Nancy hung her clothes in her closet.

(d) You hung the pictures wrong!

(e) The pictures were hung on the wall with great care.

Hang is also an intransitive verb, as in (f) and (g):

(f) The clothes hung on the clothesline, frozen stiff in the cold.

(g) The picture hung crookedly from one of its hooks; the other hook had fallen away.

The other past form of hang—hanged—is the past or past participle of hang. It is used to refer to the execution of a person by hanging a rope around the neck, as in (h) and (i):

(h) They hanged the ax murderer.

(i) The ax murderer was hanged.

Fortunately, hanged is used much less frequently than hung.