well wrote:
I have never canceled one of my credit cards, but my understanding is that it hurts your credit score if you cancel a credit card.
Closing a credit card will ding your credit score for a few months, likely 5-15pts, so not a big deal. If you're churning cards and trying to exploit points/miles/benefits, this could catch up to you. However, with most desirable cards now you get free credit checks so you can track what's happening if you're really churning.
No reason to continue to pay an annual fee on a card to avoid closing it (if that's the situation you're facing). Typically when you call to "close" they'll pass you to a business retention specialist who will waive the next annual fee or give you nice benefits for keeping the card. Always put it to the company and protect yourself.