This problem can generally be resolved by paying a past due balance or changing your payment options.
You can check your Xbox Live bill online here.
Xbox Live also allows you to purchase prepaid codes if you do not have a credit card!
If you're having problems checking your bill, or changing your credit card information, call Xbox Support at (800) 4MY-XBOX or (800) 469-9269 from 9:00 A.M. to 1:00 A.M. Eastern Time.
You can also use their Community Support Chat, Microsoft Support Chat, or request a callback from an Xbox support agent via this web page.