What about using credit cards to pay online? How safe is that?

With billions of dollars in online purchases every year and low fraud rates, credit cards are a safe way to pay online.  It is easy to dispute a charge if there is a problem with the product.  In the event that your credit card number is stolen, leading U.S. credit card brands protect you, with policies like MasterCard Zero Liability and Visa Zero Liability.  However, these policies can’t prevent the hassles of finding and reporting the problem, arguing it really wasn’t you and replacing your card (and there is some fine print to watch out for, like paying your bills on time in order to be covered).   
If you are concerned about those risks, try one of the safer options. (See, What is the safest way to pay online?)   Also, be aware that you are usually responsible for monitoring transactions in your account to receive the Zero Liability benefit; and debit cards, cash, checks and money orders often always don’t offer the same kind of protection.