Regarding carrying a balance: I have never carried a balance and have excellent credit. Carrying a balance really isn't necessary.
For someone with no other loans, they will have nothing reporting to the credit bureaus if they don't let a balance post. I never said carry a balance, which would imply paying interest.
Right - paying off a credit card in full as soon as the statement posts (or just before it is due, usually about 3 weeks later) is not "carrying a balance." It is just letting a statement post at the end of the month. I always let the statement post, but have never paid a cent in credit card interest because I don't let the balance "carry," as in pay less than the full amount due and push some portion of the principal to next month's statement.
On a couple of occasions, I paid it early because if I let it push to my balance it would actually show I was using too much of my available credit. In general, you want to show you use your credit, but use less than 8-10% of it (demonstrating you are a good customer because you use the product, but do not just take every bit of credit available to you, which is indicative of people who are credit risks). Once I had to put a $10k+ work airline ticket on my personal credit card, which pushed my credit utilization rate above 10%, so I paid it as soon as I was reimbursed, without waiting for the statement to post.
Generally, though, paying anytime before the due date means that the credit card company is giving you a 0% interest loan for a few weeks. I see how reason not to maximize on this and pay the day before it's due, no earlier, and let all of my extra cash in the meantime earn money for me in investment accounts.