Maybe you need to clarify your question a bit. Paypal is one of the few services that does allow you to checkout without filling in a bunch of details. I purchase things every week using Paypal and all I have to do is log in to my Paypal account and click pay now.
Obviously, if there is a physical product that needs to be shipped by the merchant, you will at some point need to provide a ship-to address. How else will the merchant know where to ship your product?
There are also bitcoin transactions that offer a bit more privacy. Bitpay is one that I use for people that want to pay with bitcoins. It is similar to Paypal except your customers do not need to have a Bitpay account to pay, just bitcoins. Is that the sort of thing you are looking for?