I always highly discourage people from using their debit cards online. Why?
If your debit card is compromised a lot of very bad things can happen to you even if you eventually get all the fraudulent charges refunded. For example in between the time the card is compromised and the time you figure it out, you could be bouncing checks all over town. And after that its up to you to fix your credit rating and convince your land lord or mortgage company it wasn't your fault
I never use anything but a credit card online because my liability is limited and it can't backfire into other areas of my finances like the debit card would. And credit card != pay later. There is nothing stopping me from buying now and paying off at the next statement
Very true, but like I said, most people I know don't have a CC anymore, if ever, or they only use it for fuel or some such. That sort of thing is falling out of fashion(and good riddance).
There are safer alternatives for payment options these days too, I almost never buy from anyone but Newegg or Amazon(directly) for example. Savings not worth the risk. When I do it's via paypal or one of the one time use card services online. Very good points though.