Ancestry.com Charging credit card AFTER cancellation Internet, Internet

Ancestry.com contined to charge my credit card AFTER I had cancelled their service. After I called them and spoke to their Supervisor Laura, Ancestry.com would not reimburse the extra charges because they said that they did not see a "cancellation" in their system (despite me cancelling my account online months prior).  I argued that it is not my problem that their system failed to send me a cancellation number, but they did not care.  Thinking about it now, I realize that ANYBODY could cancel their subscription online and be told "Oh, sorry, we didn't receive your cancellation in the system" which gives them the excuse to keep charging you - or should I say - ripping you off.  When something like this happens, what legs do you have to stand on as a consumer?  As a consumer you are at the mercy of companies who can easily continue charging you because they now have your credit card information, even if you cancelled your account!  I know when I cancelled my subscription (I took note of it in a schedule planner) and for this very reason Ancestry.com is a scam.  I would NOT recommend giving them your credit card or account information.  It's one thing to continue charging me in error, but it's another thing not to reimburse an honest customer.  That's called theft.  Beware!!