I always remember what finance professor used to say about credit. He was a big proponent of it being amazing but dangerous in foolish hands. Like BrianH mentioned, if you get rates on loans or whatnot anywhere near inflation, thats just giving you monetary freedom that essentially pays for itself over time. My favorite quote from said professor when he was talking about investing at a higher rate of return than your cost of capital, "Why the hell would I pay of my mortgage, its like free money!" His point being, if you are locked in at a mortgage at around 4-4.5% and can get returns through investments of 5%+, why the hell would you pay it off, you are just reducing your good leverage. Now I realize there are caveats, not everyone invests well, ARMs, job uncertainty, etc... But his point is still sound.
The reason Ramsey's message resonates with so many people is because his approach is like a lot of his listeners: Simple. Of course responsible people can manage debt, but as a society we are overrun by people who know no better than continually living beyond their means. Some people grow out of it, as I have, but others don't learn the lesson on their own. Thus they need simple rules when they finally decide to turn it around, carefully constructed into brief radio segments. "Don't use credit cards" and "Don't own cars whose purchase price totals more than half of your household income" are both extremely simple rules that will appeal to most people.
The other thing Ramsey says is "Don't get your financial advice from broke people." Whether you agree with his exact system or not, what he teaches is pretty sound advice. Don't spend more than you make, don't buy it if you can't pay cash for it. Live on a budget,have a plan and an emergency fund. Really not bad advice. I know more "simple" people who are wealthy than I know "sophisticated leveraged out the ass" people who are.