No, no, no!
Here's what I know. A friend of mine had some delinquent student loans. It had been 6 years that they were delinquent. She had a windfall of money and paid off the delinquent loans. Guess what? The student loans, instead of falling off of the credit report in 1 year like they would have (because of course, debt only stays on your credit report for 7 years), stayed on her credit for an ADDITIONAL 7 years after the "last transaction date." Which was, of course, the date she paid off the loans. So basically she screwed herself by paying off her loans.
My advice is this. Call your creditors and negotiate a settlement with them. GET THE SETTLEMENT IN WRITING. Part of the agreement should be that they report the amount paid in full as of the date is was last due. For instance, if you stopped paying on the credit card 5 years ago, they mark it paid in full 5 years ago to all 3 major credit reporting agencies. If they won't do that for you, then there is no point at all in paying them, because you're just putting bad credit on your credit report for several years longer than it would have been otherwise.
Here's the thing. Yes, you owe your debts and it's a good idea to pay them. However, there is a contract in place before you ever receive the credit card. The contract says that you pay them, and if you don't, they can unleash hell on you in the form of collections agencies and negative reports to the credit reporting agencies. You didn't pay, they've unleashed hell. Really, in a contractual sense, you have paid your dues. If you want to be nice about it and pay the actual money back to them, they need to be nice about it and help you out with the credit reporting agencies. Just so you know, they've probably already written off your account as "bad debt" and have received a tax deduction for it, so in essence, they've been paid back. This is free money to them at this point. So - before you send them a dime, they need to put in writing that they will mark your account paid in full as of a specific date (the date it was due). As in, "Oops, Experian, we've been reporting this lady past due for years, and she was never past due!" If they won't do it, don't send them money.