I work for a financial institution so I can tell you you are not alone. However when a store whether it is brick and mortar or online gets hacked cards do become compromised. In that situation your financial institution should cancel the card and reverse the fraudulent charges. Institutions will generally receive a list of card numbers that were potentially compromised when the files were hacked at the merchant. Some institutions will wait for their member to call them and stop the card due to erroneous activities and others will automatically stop the card to prevent fraud and reissue new ones.
The best way you can protect yourself is to make sure you use SSL sites (which will have https up in the browser window or a little yellow lock down on the right hand corner), sign up for online banking if your financial institution offers it so you can watch the transactions affecting your card and don't be afraid to use the card. The fraud measures that are in place these days are pretty effective at stopping most major fraud as it happens.
Hope this helps!