Not that you need to give too much details, but is this storecards, credit cards? They'll have a customer services phone number on the back.
If they've been sending statements to an old address, my worry would be that your debt has been increased by charges for non-payment, and added interest....? You will have to know who you owe and how much, so you can consolidate the debt, perhaps with a loan, and pay it off.
Meanwhile, not paying will really not do your credit rating any good at all.
However, depending on how much it is - go to our bank and ask if they will make you a loan so you can pay them all off (the bank will probably say that the loan is conditional on your doing that!) but it can be a great deal cheaper than keep on paying card rates.