When I first realized I had been scammed (for much more than I expected!), I felt totally helpless since, after all, I had voluntarily given over my credit card details to a site offering pirated content. But as it turned out, there were ways for me to get every last cent of my money back. So if you got sucked in by these people like I did, then here's the thing to do (I learned this the long way):
1) Immediately CALL YOUR CREDIT CARD COMPANY and put a stop on all pending charges and get a new card number issued. Your credit card and personal details WILL BE MISUSED, so make sure you do this right away, before you get charged by companies you never heard of, like adult porn sites. Some people try to cancel billing with these sites directly, but it is often very hard (if not impossible) to reach them. Furthermore, even if you do manage to cancel or block the specific billing companies, the thing you need to remember is that they ARE crooks and now have your credit card details. Are you comfortable with that? I sure as hell wouldn't be!
2) Call your bank, tell them you have been defrauded by this merchant, and did not receive the promised goods - and then request a CHARGEBACK. Now you probably DON'T want to tell them you were trying to download a pirated version of some new software or a DVDRip, because that's certainly not going to help your case. However, if you tell them you were trying to find a hard-to-find manual, essay, drivers for your old printer or anything along these lines, you'll definitely be in the clear. Next, the credit card company will investigate the matter and easily realize that their service is in fact a scam, which will not only get you a full refund, but also hit them with a chargeback penalty of approximately $15-$35 USD. These scams run on thin profit margins, so this strategy will quickly put them out of business.
Just remember to be aggressive with your bank - don't take any crap! VISA and MASTERCARD actually profit from your loss so tell them that this is fraud, point them to related posts on complaintsboard.com and others like it, and make it clear that thousands of people like you have been ripped off. Eventually these fraudsters will lose their ability to charge money and the world can be a better place.
Here is more information about the chargeback process: