This is a hard-to-kill-off myth. Closing accounts typically won't help your score and could possibly dent it, says Trey Loughran, president of personal information solutions at Equifax. The results can shorten your credit history eventually and leave you with a smaller amount of available credit, both of which can harm your efforts to build better credit.

The length of credit history shows how seasoned of a borrower you are, so the more positive experience you have, the better. Having more available credit helps to keep your utilization rate low. The utilization rate is how much available credit a borrower uses; the lower the percentage, the better.

"Say you have $100 in debt with $1,000 in allowable credit across multiple accounts and you close a credit card with a limit of $500, then you doubled your utilization rate from 10 percent to 20 percent," Loughran says.