I order online. I think it's safe as long as you are dealing with a reputable vendor and their security certificate is up to date and valid. Of course, you may run into a man in the middle attacks or something like that, but that's why most credit card companies will work with you to remove fraudulent charges. Besides, you don't need to shop online to be a victim of identity theft. Look at all the companies (besides retailers) who's databases have been hacked revealing customers social security numbers or other identifying information. You could just as easily use a credit card at a gas station and without you knowing, a skimmer could have been attached to the card reader.
Anyhow, visit reputable sites, read the fine print, and keep an eye out for anything that looks suspicious.