From what I've read, paying off your cc bills every month won't hurt your credit. The cc companies typically report your amount owed at the close of your credit cycle, before the actual due date. So even if you don't maintain a balance, your credit report should still show that you owe something on your cc every month. Now if you pay everything off before the close date, then it'll be reported as zero balance.
The Fico scores are determined mainly by several factors. Mainly debt to credit ratio, age of accounts, # of recent inquiries, etc. I think the most important is the debt to credit ratio. It's best to keep it down below 34%. So if you have a credit card that you don't use, don't close it. In most cases, it'll lower your credit score when you do.