Well, a friend of mine asked me to use his username and password to login to pay something for him on GoDaddy, registering a new domain.
After registration, my credit card information is still available as a payment method in his account and don't want to be deleted, it says I must put another payment method before deleting the only existing one.
How can I force delete my credit card information?
If your friend is indeed a friend, then get them to provide their card details so you can remove yours. It's unlikely that Godaddy (or anyone else) would want to continue providing you with a service unless they have at least one payment card to charge. If you don't do this then you could end up funding your friends website.
From a totally different perspective; from a totally legal view, the person who is PAYING for the site or domain, is the person who OWNS that site or domain. At least that's the UK law. So theoretically, if your friend is not forthcoming, you could legally shut the site down or sell the domain. Not that you would of course.
When all charges have been prepaid and the customer does not want autorenew there is no justification for GoDaddy's practice of disallowing a credit card being deleted unless another is provided. In these circumstances retaining a customers credit card details on file when the customer wants it deleted is a sleasy and risky business practice.