1)Do you count debit cards as credit cards? That's what I use, a debit card that deducts from my checking account.
2)As long as you have a bank account and e-mail address, you can enroll with Paypal. It takes a couple of days to get registered with an account because they have to verify your existence and bank account.
3)Lots of vendors will take checks by mail, money orders, and etc. This, of course, takes longer to process your online order than instant payment, but lots of people prefer it this way on both sides of the transaction.