I must say, asking for the password to facebook is just plain insane. I figure they need the facebook to actually log into the persons account because they have set their stuff to private viewing. However I just cant understand the reasoning. Someone might be a serial axe murderer and post about their latest kill on facebook, but it is still not within the jurisdiction of the company you work for. What you do in your spare time, be it badmouthing your company or stomping on kittens and as a result what you post on facebook is of no concern to your employer.
Given that I barely ever even use facebook, I almost feel like sure, they can have my password. But I am scared what will happen when they just up and hi-jack the account, like what happens to other people who carelessly give out their passwords.