“Cutting Your Credit Card Debt: How to Get Started”
Cut your credit cards. There is a special slot in most shredders for them.
If your point is to stop using them until you have paid off the balance and request new cards, I agree.
But, you don't want to close all your credit accounts. That will hurt you later when you apply for new credit (mortgage, car loan, etc.)
Instead, I'd consolidate onto 1 or 2 of your cards -- the oldest accounts and/or no-fee accounts. Don't worry about interest rates... your goal is to pay them all off each month and never pay any interest.
Keeping the oldest accounts boosts the length of your credit history. Keeping the no-fee accounts are free, as long as you use the card about once a month to keep the account from being closed due to inactivity.