PayPal recently changed their policy about this. I was worried about the same thing. Now, they offer people who don't have PayPal accounts the opportunity to pay with their credit cards.
PayPal offers a customer the opportunity to pay using a credit card up to $2,000. That's $2,000 total, not on one purchase. Once the client has charged $2,000 (on any combined number of products) they must then sign up for a true PayPal account. So, if I, as the customer, used PayPal and paid with my credit card for a $100 item at one site, $300 at another site, $50 for something else, etc. Once I hit $2,000, PayPal wouldn't let me use that credit card anymore. I'd have to then sign up for a "real" PayPal account or use a different credit card
There is no cost for getting a PayPal account, but they do have to provide bank account information.
Then there's always ClickBank. It's more expensive than some others, but it's really easy to setup, the intitial fee is only $50, and they handle ALL the aspects of your affiliate program (including sign ups, tracking, payments, etc.) if you choose to have one.