rmcalis makes a good point, but if you use PayPal on eBay, the seller never sees your CC#. Even then I will usually use my American Express card since they seem to have better fraud detection.
They have called me on my cellphone several times within minutes of making purchases that did not seem to fit my usual shopping pattern?
A couple of years ago, they called me and said that someone had tried to used my AmEx card to make an internet purchase from a Women's Fashion shop in Los Angles. They decline the transaction and immediately called me. How someone got my AmEx card number is beyond me, but AmEx immediatley canceled my old card and sent me a new one within a week.
The only thing that I was suspicious of a company in California that I made an internet purchase from with my AmEx a month earlier. The item I purchased arrived from somewhere in China? This was not an eBay purchase and I used PayPal, but I think the delay in trying to use my card number was probably a strategy so that I would not get suspicious or link the fraud charge to them.
...Rich