As someone that's sold services and webapp subscriptions online for about 8 years now, I've seen a lot of payment fraud, mostly in the form of signing up with stolen credit card numbers. I've managed to manage the fraud with risk scoring systems, automated calls to customers during checkout, etc. so that I stay under a 1% chargeback rate.
What I'm wondering is what other startups do about the payment fraud they detect. Do you ever report it to the police? Your police, or if you have a pretty good idea of the identity of a scammer, to their local police? To the FBI? What about Visa and MasterCard themselves? Do any of them actually care?