Sunbeem here, in the midwest of the USA-
I have heard many places that it's true about credit affecting mortgages- having good credit will get you a much better interest rate. When I was in high school, I was encouraged to get a credit card in order to start building good credit. So I did. Unfortunately, Yvaine is right- the whole system is broken. It rewards you for having debt that you
manage, and punishes you for avoiding debt.
I tried to get a small car loan after college, and my credit
history wasn't good enough- even though I paid off my credit card in full every month (meaning I never had to pay interest or late fees), and had a really high credit
score, and had had the same credit card for over 3 years, and had accepted a good job in a stable industry, US Bank told me that since I only had 1 credit card and no other kinds of debt, that I had "too limited" of a credit history. I ended up getting a loan co-signed by one of my parents, and because I had a good credit
score I got a very slightly lower interest rate than I otherwise would have.
In the US, do you pay interest if a credit card is paid off in full at the end of the month? I have heard this so often from Americans.
I only start paying interest if I do not pay my full bill at the due date, which I always do.
Credit cards in the US: You use the card to buy stuff. At the end of the billing cycle, they send you a statement and then you have another few weeks until the due date. If you pay the full amount on the statement, there will be no interest charged. The other option is to pay the "minimum" payment, which for my card has ranged from $10 to $30 a month. If you pay the minimum payment, you will not be "penalized" per se, but you will be charged interest on whatever remaining balance carries over into the next billing cycle. Completely
missing a payment is what hurts the credit score the most. I'm not sure how the monthly balance factors in.
One nice thing about credit cards is that they allow one to buy something and not pay for it until six weeks later- for example if my billing cycle started on June 1, I could buy something June 1, and it wouldn't show up on my statement until July 1, and then I wouldn't have to pay it until about July 15, and at that point could pay it in full and have no interest. Meanwhile my money would be sitting in my interest-paying checking account and giving me a few extra dollars.

I think Dave Ramsey's "cut-up-your-credit-cards" advice is good for people who have racked up a lot of cc debt or don't have the discipline to avoid impulse purchases, etc., but he is a bit over the top as having a credit card is a good tool for someone who uses it responsibly and is cautious enough to read the fine print and not get into a credit card with bad terms & conditions.