For sites that don't allow you to close your account, log in and update your profile with fake information. That way if the worst does happen, hackers won't get much.
You should also take a look at the list of passwords in your browser. If you notice that they're all the same, or you have a lot of duplicates, that's a warning flag.
Make sure that the accounts you're abandoning don't have the same password as accounts you're keeping. And make sure unimportant accounts don't have the same password as your important accounts like finance, email and social media.