A pair where for the longest time, I’d try to find other words instead of having to figure out which one is correct.
But “hanged” and “hung” is actually pretty simple. They are both past tense of the verb “to hang.”
“Hanged” is used for people. “The criminal was hanged.”
“Hung” is used for objects. “I hung the painting in the living room.”
This distinction is relatively modern, within the last few centuries. Perhaps the distinction will be lost again in the future.