A credit card offers a number of advantages if you use it the same way you would use a check card or cash, i.e. don't use the credit aspect and carry a balance:
1. fraud protection - if someone steals your card or number and uses it you are not liable, to the best of my knowledge a check/debit card offers no such protection. Likewise if you buy something and it is defective, not delivered, etc. you can dispute the charge and not pay.
2. free credit - you get a months free credit until you actually have to pay the bill. In fact, I use 2 cards, 1 card has a billing date at the beginning of the month 1 on the 16th, from the 1st - 15th I use the first card, from the 16th - end of the month I use the second. This way I maximize the free credit that I get.
3. Money is not constantly draining from your checking account. You pay once or twice a month allowing you to keep the money invested somewhere else earning interest (I admit a pittance these days) during the month.
4. You can usually find a free credit card that gives you something back. For example, my parents have a Shoprite American Express card. They get 1% back (in the form of a Shoprite voucher) for general purposes and 3% back for Shoprite purchases. Since they shop in Shoprite anyway, the vouchers are as good as cash for them. They carry no balance and use the card for eveything that they can, so over a year it is a decent sized sum of money for free.
5. It is easy to keep track of your purchases every month. You get a bill itemizing every purchase. If you use cash it is easy to forget.