Payment API built for developers to process credit cards. One can even process payments via curl!
Simple article on how to set up a PayPal account that is not easily or directly linked to a person's name.
Vaguely illegal sounding article on how to use PayPal anonymously. Involves gift card based activation, a clean IP, and an anonymous card that can be used as a bank account. US specific.
Sell on facebook and other places. They handle everything for 7% plus 3% + 30c for card processing, but they'll take cards for you, no merchant account required, through elavon.