First of all: cash is king! And like someone else said above - I only use debit to get cash from an ATM.
Whenever I purchase something on the Internet, I use prefer using credit card (not debit). If something happens, such as technical error that bills me 100x for one amount, worst thing that can happen is that the credit card gets maxed out for a few days. If that happens with my debit card, it means I could be without money until the bank sorts it out.
Also, when I buy airline tickets (or any expensive items), I always use credit card. If the airline goes bankrupt after I have booked the ticket so that I can't travel after all, I won't have to pay for it in the end.
One thing I always make sure of though (when using credit card, that is), is to pay it back before they start charging interest. This is very important. And if I won't be able to do so, it means that I can't afford it in the first place (and then I won't buy it).