The statute of limitations varies by contract and state.
Here is a chart that will help you find your exact answer: http://www.expert-credit-advice.com/statute_of_limitations.htm . A credit card will likely be categorized as a revolving account. Also, FYI….There is a separate statute for the amount of time it can be reported to the credit bureaus. If the debt is past the statute of limitations you have no legal obligation to pay. If a company purchases the debt after it has passed the statute, they can try to collect but again you still have no obligation to pay. Either way, they can continue to say you owe, unfortunately it is your obligation to advise them in writing that the debt is time barred and you demand they cease and desist communication.
If they continue to harass or try to collect after receipt of this document, you can sue for damages and you will probably win. The term used for these scoundrels is “Junk Debt Buyers” or “Zombie Debt Collectors” and here is a fantastic article :
http://www.expert-credit-advice.com/junk_debt.htm .
You may also want to file a complaint with the FTC or your state attorney general as well. Settling the account after it has passed the statute may allow the item to be re-reported and stay for another 7 years so be careful!