Just because you paid off that credit card doesn't mean you're through with it! Call the company and ask that your account be closed. You don't want any temptation, as in asking for a new card to be sent. If, in the future, you think you need a new card, start all over. And think about it first.
While you're at it, cut up the card and use the pieces to scrape food from dishes or smooth soil around plants.