This headline states the obvious, right?  BUT, some consumers are surprised to learn that closing a credit card account after it's paid off can result in a lower FICO credit score.  The way to avoid this problem used to be paying your account down to zero but keeping the card active.  But times have changed. 

According to this USA Today article, even maintaining zero balances on open accounts may come with a price tag in the near future:

In the past, the most effective way around [dissatisfaction with a particular credit card] was to pay off the balance and stop using the card. As long as the account remained open, your credit score would remain unscathed. But increasingly, that strategy carries a cost. In response to credit card reforms that take effect Feb. 22, credit card companies are looking for new ways to raise revenue. Some are adding annual fees. Others have started charging inactivity fees if customers fail to use their card during a specified period.

As new credit card regulations take effect, be sure to follow your statements closely and watch for new terms and conditions from your bank.