Nope...according to PayPal, I can not accept credit or debit cards. If I upgrade to a Premiere or Business account, I can, for a fee.
Personal Account
Ideal if you shop online. Make secure payments on eBay and merchant websites using your credit card, debit card, or bank account
Premier Account
Perfect for both buying and selling. Make secure payments on eBay and merchant websites. Plus, accept credit card, debit card, and bank account payments for low fees.
Business Account
The right choice for your online business. Accept credit card, debit card, and bank account payments for low fees.
Originally, PayPal let "free" users accept moeny for up to $400 per year. I guess that part's gone now.
Still, as a "personal account", you can accept PayPal e-checks. They buyer will have his bank account debited, and you get the money, only a bit slower. With credit-card backing, the money is transferred "instantly" from buyer to seller, with a few dasy added for PayPal to keep the float. What PayPal does is still debit the bank, but if the funds don't show up fast enough (for PayPal), they ding your credit card, instead.
So neither the buyer nor seller need a credit card, put PayPal still licenses the seller to use the credit card logos. If you, as seller, are paid by echeck, I don't think PayPal does anything except keep the funds for a few days for the float.