Customer rights regarding credit card data retention

Hi,
I do apologize if this is the wrong group for this type of question, in
which case I'd appreciate a pointer to suitable groups or net
resources.

Here goes:...
Having had the dubious pleasure of being a victim of fraudulent charges
to my credit card, I decided I no longer want to allow any e-business
to store my credit card details on their computers in any form. I want
any trace of my credit card details to be erased as soon as they get
the CC company's OK for the transaction.

I wondered if anyone knew what was my legal position on that as the
credit card owner. For example, are businesses obliged *by law* to
obliterate any such data once a customer requests them to do so.

Also, I have recently come accross two annual-subscription based
services, whose 'terms and conditions' fineprint revealed that...
(guess what?...) - the subscription will be automatically renewed at
the end of the 1 year subscription term. Unless I *then* demand
otherwise I suppose, but even that is not clearly stated in that text.

Beside being more-than-slightly disgusted by businesses who try to make
money in these ways, I am wondering if I can insist in advance that no
renewal would take place without my prior explicit consent, and more so
any charges to my credit card, based on some legistlation, rather than
just my bargaining position as a potential customer.

What's the legal state of affairs on that?

Thanks a lot in advance,
Ben

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