Pay your credit card bills in full and on time for two main reasons. First, if you do not pay your balance in full, you will be subject to interest. Any interest that you pay will negate any free travel that you book on points. This game only works if you do not incur interest charges.
Second, a credit score decreases (and therefore the ability to earn free travel through credit cards) by paying a bill late. Stay on top of payment due dates, give your payments enough time to get there by mail, etc. If you think your payment won’t get there on time via the mail (the more credit cards you have and use the harder it is to keep track), go to the bank and pay the credit card, or pay it over the phone or easily pay it online.
I have gotten into the habit of constantly paying my Chase bills on the due date either online or at the actual bank. I feel safer about doing this than mailing my payments. Doing so gives me more time to delay before paying the bill and more importantly, it gives me more time before telling Rob the amount of the bill.