I have not made a credit card payment in 9 or 10 years. They called and said I need to pay them or go to court. I have no means to pay them right now. Do I have any rights? What can they do?

Find out what the statute of limitations are for your state.

Very few are 10 years or more, some are as little as 3.

Wait until they take you to court but make sure you go or they could win the full amount.
If you haven't paid them in 9 or 10 years then most likely the statutes of limitation has ran out, IF you send them one single payment it does away with the statutes of limitations and you are back to square one all over again and they will keep after you.
Send them a print out of the statute of limitation for your state.

One other suggestion, the letter should have stated that you have 30 days to dispute the debt.

Once about 25 days has passed, contact them and request validation of the debt. It will cost you about $6 or so, but mail the request certified mail, signature required. This will buy you some time to research the statute and make sure that it has expired.