Who is actually asking for FB passwords? I doubt anyone actually is, and if they are it's part of a scam involving the promise of employment to desperate people.
I've read about police and city agencies requiring social networking passwords to be given up. Same for departments of corrections. Here's a photo of a job application for a clerical position at a police dept: http://i.imgur.com/hWsZT.jpg (From this reddit thread: http://www.reddit.com/r/WTF/comments/mtenb/wife_came_across_...)
It's apparently quite common. The real kicker is when they also include a non-disparagement agreement in the hiring process, so that they can easily fire you for non-publicly posting about your job.
Combine psychotic parents, "cyber bullying" (a crisis de jure), morals clauses in contracts, "think of the children" attitude, and sometimes tyrannical administration, and you get crazy stuff like this.