Not so fast. A credit card with a high limit is a good safeguard against a cash emergency. As happened to me a couple of years ago, when a sudden death had the family scrambling to get to the funeral. Six round-trip airline flights is a chunk of change, and we had to book them in 2 days.
But you won't get a high limit if the computers think you're a poor customer, an that's what their idiot programs will think if you always pay off.
A better strategy, in my opinion (as informed by one of the guys who wrote the idiot program in question), is to charge something big about once every couple of years, and take 2 to 3 months to pay it off. Yes, it costs you a little interest (about 2%), but to the computer you now smell like a rose.