Between November 27 and December 12 of 2013, Target stores company-wide were hacked, compromising up to 40 million credit cards. The breach does not include purchases made online with Target, only in its retail stores. If you've ever used your credit or debit card at Target in the United States, it's highly recommended that you get a new card and close your current account. Canada Target stores have not been breached, however, because of their requirements for a digital chip in the card itself and a PIN. Without these two factors, a transaction can't be made. Banks will help with issuing new cards, and some banks including Chase are automatically sending new credit cards to potential victims of this attack.
If you want to protect yourself against credit card fraud in the future, there are some things you can do. Some banks will actually send you a notification each time the credit card is used, either by text or email. This will tell you right away if the card has been used by someone else. Contact your bank to find out about these options. There are also "one time use" credit cards that will be good for only one transaction, and cards that will only work at a single merchant.
While this attack was of Target retail locations, this event has also raised concerns about the safety of using credit cards online. The truth is that it is safe to do, as long as you make sure the URL in the navigation bar of the browser matches the site you're on, and that you're using "https" so that the transaction is encrypted. It's also important to make sure that your computer is up to date with all the latest security patches, and is free of malware.
If you want to find out if you've been the victim of identity theft, you can check your credit report free once a year at AnnualCreditReport.com. Avoid FreeCreditReport.com though, since it's not actually free.