First you need to Back up your account and check to see if you have any other accounts or APPS where you have used Facebook to login with first before you do anything else.
There are several places you could have used Facebook to login instead of using an email and password. This is the top of many peoples problems. What if you do not want to use that service anymore .. now they have you by the balls .. or the mound.. ( we are equal ova here).
In the video - Sharon Profis shows us how to completely delete your Facebook account without losing any of your important data.
**Please keep in mind that you won't be able to reactivate your account or retrieve anything you've added. Before you do this, you may want to download a copy of your info from Facebook. Then, if you'd like your account permanently deleted with no option for recovery, log into your account and let us know. - Facebook