There are two types of risks when you buy online, having someone steal your credit card payment account information and being duped by a fake merchant Web site.
One way thieves steal banking and credit cards online is with phishing, an email that directs you to a merchant Web site that looks real but is really operated by criminals. Spyware and malware (malicious software) are nasty programs that someone sneaks onto your computer that can be used to steal credit card account numbers and other things.
For more information on these and many other threats, click on the "malware" tag shown above. Also see, What is the safest way to pay online?
For ideas on how to know if on online merchant is dependable, see How do I know if it is safe to enter my credit card information when I am shopping online?