For online shopping, a virtual credit card adds a layer of security. Some card issuers let you randomly generate a new card number linked to your account. In industry jargon, this is a "virtual credit card." Ideally, it would be a single-use number. I don't know if anyone still offers this, possibly not. If not single use, it still gives you more control. First, if you use it for one merchant only, you will instantly know where it was stolen. Second, you can cancel the virtual card number at any time — for example, when you're certain you won't need to return what you've bought. Other than #2, the only drawback is the need to keep a paper or Acrobat (pdf) copy of your sales receipt.
If you use this consistently, you needn't worry about a merchant's web site being hacked and your card number stolen. A virtual number can be stolen, but if you exercise due diligence it cannot be used after your one-time purchase.
Run a search on "virtual credit card" and you will find lots of articles and/or advertisements.