Does closing CC accounts hurt or help credit score?

I usually keep them open.

I would only cancel if you are paying an annual fee. If you have something like a chase freedom, I wouldn't close it. Just keep it open and buy a pack a gum on it 1-2 times a year to keep some activity.

If you're dead set on canceling, make sure you don't cancel the card you've hard the longest. That will mess with your average history