If your important numbers (in the US that's passport, social security, and driver license) get leaked, it becomes easier and easier for someone to commit identity theft and open credit cards in your name which you will have will have to pay with either money or a lot of time proving it wasn't really you. Or they can get traffic tickets in your name which will become a warrant for you.
And if they know enough about you (address, likes and dislikes, etc), it becomes much easier to socially hack (https://en.wikipedia.org/wiki/Social_hacking) you. Any security is only as strong as its weakest link, and social hacking has been used to get access to people's bank account, email address (doesn't sound scary but if someone has access to your email, they likely have access to all of your accounts because they can trigger a password reset, intercept it, set a new password, then lock you out), and a lot of other things.