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.
If what I've read is true, lots of places. A school teacher in my area just got fired for making a student give access to his/her Facebook account which the teacher used to punish students who had talked about the teacher.
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.
Schools are breeding grounds for this sort of thing.
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.