According to this Yahoo Daily News article, a group of high school students came up with just such a plan; they asked people for their credit card numbers directly, over the Internet. What innovation! What creativity! What stupidity on the part of the people who gave them the numbers.
Not to perpetuate a stereotype or anything, but many of the victims were apparently AOL'ers (Earthlink subscribers were victimized as well). The criminals were four 14 to 16 year old kids, all of whom went to the same high school. They rang up about eight grand worth of stuff before they got busted. It appears they were at least somewhat smart about it though; they had the goods delivered to unoccupied homes, and perhaps most intelligently, they did it before they turned 18. Heh heh.