Assume, for a moment, that the web site you've signed onto actually keeps to its privacy policy. So you give them sensitive data, such as a credit card number. Or, in some parts of the world, the simple fact that you're gay. So far so good.
Now, what happens when they go bankrupt? The database to which you have contributed is an asset of the bankrupt company. It will go to the creditors. And they are not bound by any privacy policy. Worse, often the original credits have sold the debt to debt collection agencies, who often have all the moral compunctions of a shark.
All the more reason to keep your sensitive data to yourself.