When you want to use a Facebook game or other application, you must often allow that application various privileges. For example, you may have to grant access to your personal information and you may have to ‘opt in’ to receiving promotional email messages. This is a kind of business transaction: you give up some of your privacy – and, potentially, some of the privacy of your contacts – for the right to use the application.
Once you have allowed an application to access your personal information, whoever is behind that application can also use that information outside Facebook, even when you no longer use the application. Do not rely on being able to remove information you have provided to a website or other Internet service.
Taking good care of your personal information helps protect you from identity theft, including so-called social engineering attacks (wherein someone poses as you in order to obtain information to which you are entitled as a private person, on the job or elsewhere).