I work in fraud prevention, so I can offer some points from my experience.
One type of fraud that happens a lot goes like this. Someone takes a card number (by whatever means). If the card is from a large bank with lots of cards issued (Bank of America, Chase Manhattan, Citibank, Wells Fargo, Capital One, etc.) the crooks know that there will be a lot of cards with numbers similar to the one they stole. They just use different combinations of numbers for the last 4-7 digits and get hits on other valid accounts from the same issuer. They could hit upon your card number by chance and there's nothing you could have done to prevent it, save for not owning a credit card. I see this done every day. This is just one of the scams they run. Information about how to do it is easily accessible online. There are a ton more.
Use of the internet for commerce and communication has made it harder to prevent and prosecute fraud because the person placing an order over the internet can be anywhere in the world. Try tracking down someone ordering from a computer in Nigeria (a huge destination for stolen merch) or Singapore. The chances are pretty remote. Local teenagers are an easy catch compared to the international folks.
And for every person who is vigilant or paranoid about giving out information over the web, there's someone who falls for a phishing scam or agrees to receive merchandise from someone they only know through IM or BB chat. Once the frauds have that, it's open season. They order as much as they can as fast as they can to strike before that particular avenue gets cut off.
I remember one woman called us because she agreed to receive and forward merch to some guy in Liberia, who gave a sob story over email about how he was buying shoes for kids in his area but couldn't get them shipped to him directly from the merchants. She got the shoes all right, 30 pairs of them just from our company. She also got sent to her house 3 Dell computers, 4 boxes of stuff from Home Shopping Network and 6 or 8 George Forman grills. At that point she figured something was fishy. Sadly, some people just play the fool and send the merch off to its new home, never to be retrieved, or paid for either, because the person whose card was billed will have it charged back from the merchant.
A lot of the frauds are organized, efficient and sophisticated. Even those that aren't stand a fair chance of stealing something because of the sheer volume of the problem. The Secret Service used to take a lot of info from merchants about Nigerian frauds to use for their investigations. Now, they don't even want it because it's like bailing out the ocean with a spoon. It grows at a seemingly geometric rate. The crooks share information and methods. If they find a company or bank or web site that's easy to exploit for their purposes, it gets spread around like a virus. The same stolen card numbers get recycled over and over again.
Maybe that gives some perspective on why the problem is so bad. There are countless other facets to the issue. It's hard enough for merchants and banks to keep up with the scams and the number of frauds commited. Stopping or slowing the problem overall is a whole other nightmare.
