Makes you worry where this is going to end up...
I cam sort of see how googling someone and looking at their fb to see if it is nicely private can be useful pre-interview, even if it doesn't thrill me as an idea (not least as if you google my name it comes up first with a stripper in Amsterdam - not me I hasten to add but probably wouldn't be a great starting point :o).
But then asking for a password so they can see - and that would also enable them to post or change things in your account - would be a really dangerous thing to do. What if they did do something while logged in as you that you didn't like? No proof that you didn't do it if you have given your password to them and probably no comeback. Can you imagine what house insurers would say if you had to give your house keys to potential employers - who will be strangers to you at that point most probably- and let them wander around your house when you are not there. Most would be fine but there could be some bad ones that do damage or nick stuff and there would be no comeback.
And this is only the thin end of the wedge - next they will want access to ALL your accounts - especially if you have more than one on fb (so you can't get away with having a special one for show purposes) and then they'll want access to twitter and linked in and all public forums that you post on - can you imagine how you'll feel when they'll want to know your mn nickname and then want to check out all your mm posts?
And of course if you use the same password for more than one thing (or have a system that people could guess at and extrapolate to other sites), you might discover that - be it now or a few years down the line once you've got the job and these details are lurking in your hr file and dug out by a disgruntled colleague) that they have managed to access your bank or amazon account or mn and really screwed you over on all sorts of levels.
A very slippery slope once you are being asked to provide passwords...