Even if something did get compromised, it would only take a call to the bank to stop it all. I say that lightly even though it would be a pain.
Banks make it fairly easy to report fraud on a card and get it cancelled and replaced nowadays, actually. I've had to do it with Chase and Discover and it was a 5-minute phone call. The main inconvenience was the wait for the new card.
One neat feature of Discover is that they have an online number generator that you can use for online purchases, so that you don't have to give out your real card information. Other banks may also have this.
I'd be more worried about using an unknown ATM than a card online, because of skimmers. And I agree with TimeX that I am even more worried any time a card leaves my sight, such as at a restaurant, or if I have to give it over the phone. The other day, my buddy ordered Indian food for delivery and he later noticed that they hand-wrote his full card number and information on the back of the receipt -- not very good security there.
Make sure that your client machine runs anti-malware software and that you always keep your OS and applications up-to-date, as that's probably the most common way that card information is stolen online. Logins for Paypal and any other service can be stolen the same way, unfortunately.