Netherland has proper internet payment infrastructure called iDeal: it goes directly from one bank account to the other, with no sleazy middlemen in between. That's what the rest of the world should be using, but Netherland just doesn't have the weight to push its solutions on the rest of the world, so we're stuck with crap like PayPal, Visa and Mastercard.
(I suspect many other countries also have well-working payment systems within their borders, but none have any international reach. I'd expect that SEPA would lead to a reliable internet payment system on a European scale, but that hasn't happened yet.)
In terms of the horror stories I think it depends a lot on your business. For someone like us sending relatively predictable large volume through in the mostly $25-$150 range we have never had an issue. At most we probably only ever had a $50k exposure to PayPal as you can withdraw as often as you want.