Now American Express is offering some customers $300 if they pay off their balance and close their account, but canceling credit cards could actually hurt your credit score.
And most people think fewer credit cards are better for your credit score, which measures your ability to get the best terms on a car or home loan.
"A lot of people are actually surprised that they paid off an account, they closed the account, and their credit score actually went down a little bit," said Rebekah O'Connell with Triangle Family Services.
O'Connell explains 30 percent of your credit score is determined by credit usage --what percentage of your total available credit is already spent.
If you have credit card balances adding up to less than 30 percent of your available credit, your score goes up.
But O'Connell says if you close accounts, "it might actually lower their score because their overall credit usage goes up."
Some shoppers find this hard to believe.
"If you pay your bills and you have good credit score, how to do you hurt your score by paying the bill off," Raleigh resident Abdul Jabal said.
But closing an account can hurt your credit score and lenders are demanding higher scores before making loans.
Credit experts say closing accounts may be a good move if people are afraid they will not have the discipline to keep balances under control.