I can accept credit cards directly on the site via PayPal Pro. My site is membership subscription, and because of my nature of my site, I don't have any charge back yet. I have a 30 day money back, so customers who want to cancel just email me.

When people mention that they use PayPal, they should say if they are using PayPal Pro (on seller's site) or the PayPal Standard (on PayPal's site). The user experiences between the two are very different.