For you, this means you have to make sure your computer is as secure as possible. You don't know which sites you visit run Drupal or something else, so avoiding certain websites isn't an option - my site doesn't run Drupal if you were wondering.
When hackers get access to a website, they'll add links to malicious sites and programs, slip in malicious ads or even put automated attack code on the legitimate site itself. These attacks affect computers that haven't installed regular updates.
You always want to make sure Windows, your browser, Adobe Flash, Java and other key programs have the latest updates. You also want to be running up-to-date security software to warn you about malicious programs that might try to install.
If you set up an account on the compromised site in the past, the hacker will have access to your email address and password. Again, this is why I tell you to create one password per website. Click here for my secret to making strong, unique passwords.
With all the data breaches happening, it's likely you've changed your passwords recently, and hopefully made them unique. If you haven't, and you like to use one password everywhere, now is the time to start changing them.
Hackers could also use the compromised site's mail system to send you legitimate-looking phishing emails with malicious links. If you're used to getting mail from the site, it's going to be very hard to spot a fake.
Here are some things to look for in a fake email, but generally avoid clicking links that have to do with your account or that would ask for other sensitive information. Visit the site directly to take care of things like that.