It is absolutely possible to delete your Facebook account and profile permanently. It is harder to find (I had to search the help section for "permanently delete" or something), and they give you two weeks to change your mind. Of course, they still have tons of information about you, but I am tired of hearing people claim that you can only deactivate your account.

I deleted mine two years ago, but not before downloading my data. I haven't ever gone through it, but now I am interested to see if they included call logs and stuff.