Login info should be for the user, not for the site

I have had this come up a few times. A user wants to buy something on another webstore but can't use the same login info. Logins should be for the customer, not for the webstore. I have a customer that buys from 3 different sites and has to have 3 different logins. I think it would make sense that they can login to any webstore with 1 login.