Despite the legal protections afforded to debit card users, there remain safety concerns that don't exist with credit cards. While credit card fraud can create short term hassle, the hassle from debit card fraud can adversely impact the victim's financial life for many years.
For those who therefore avoid debit cards completely (like myself), the payment methods available in most stores are cash, checks, or credit cards.
Cash is relatively fast, sometimes faster than credit cards. But prices rise, the government won't put larger bills into circulation, some vendors are leery of cash (especially larger bills) for fear of counterfeiting, and many people are uncomfortable carrying enough cash to handle all the transactions they're likely to make in an outing. Bills and coins are also notoriously dirty. Cash transactions produce the smallest audit trail--which may be a benefit or a detriment depending on your perspective.
Credit cards can be problematic for some. Many people are overextended. Some have difficulty controlling their spending when using credit cards. Even folks who use credit cards as a convenience and pay everything off each month might have reasons to limit what they put on credit. Some are trying to limit how much credit they utilize during the application process for a loan or mortgage. Though less common now, there was once a popular belief that life's essentials (like food, clothing, and consumable household goods) should never be bought on credit. The electronic processing of transactions is not without its problems--I reconcile my credit card statements thoroughly and find significant errors at least once a year.
Checks have a lot of nice fraud protections and produce an audit trail that's useful to the payor. I haven't seen any credit or debit cards with a little display showing the user their balance. But every time I open my checkbook, I see the running total in my check register, and it's trivial to update it as I write out a check. And my total is more up-to-date, since it includes pending transactions that haven't posted yet.
In summary, every method of payment has pro and cons. There is no method that is universally right for every person for every transaction.