The only problem with debit cards is that some places won't accept them. You can live just as "debt free" with credit cards---you just have to have the discipline to pay off the balance EVERY MONTH---IN FULL.
I have one credit card for just such occasions. However, it is very rare where such a card is not accepted as any other credit card would be.
I have not needed the services of my credit card in over 18 months. It changes the way that you plan for major purchases.
Unless I travel out of the country, I just don't experience that very often. The only time I've had it happen in the last couple of years was at a rental car place in Hawaii. A better argument for credit cards is that you can accumulate airline miles or rebates with them and you have more recourse if you are the victim of fraud.