1. You don't have to pay for stuff up front. More cash in the bank means more interest earned and/or less mortgage debt to repay.
2. You can earn loyalty points and redeem them for good stuff. About half of the flights I've taken in the last four years were business class redemptions, courtesy of credit card points.
3. You get travel and items automatically insured and/or bonus warranty if you use your card to pay. Again, if it's a feature you get for no extra cost, why not?
It also pays to do your homework to find out which credit cards suit your spending pattern the best. A free credit card might sound like a good deal up front, but offer nothing in the way of a loyalty program. One of the cards I use I pay a small premium for, but what I get in return far exceeds that small investment.