Should I close a paid-off credit card or keep it open with a zero balance?

Usually keep it open. Closing a card removes its credit limit from your total available credit, which raises your overall utilization ratio and can lower your score. It can also eventually shorten your average account age once the closed card drops off your report years later. A card sitting at zero, meanwhile, quietly boosts your available credit and helps your utilization.

Exceptions worth considering: a high annual fee that isn't justified by rewards, or a real risk you'll overspend on it. If the fee is the problem, ask the issuer to downgrade you to a no-fee version, which preserves the account history and limit. To keep an unused card from being closed for inactivity, put a small recurring charge on it and autopay it in full.