I don't want you to store my credit card info

If given the option, I never have online vendors store credit card information. The only exception to this rule are well-known vendors I believe I can trust. An easy example of this is Amazon. What are examples of vendors I definitely do not want storing my CC info? Well, an easy one that came-up recently is the local parking service I use by the airport when I travel. I just don't trust them with anything other than providing a spot to park my car. I see plenty of websites that do have an option to not store CC info. Are there consumer rules requiring this option? It would seem this should be common sense. I mean, just because someone has a website they should not be entitled to store data you do not want them to have.