I'm not sure how common it is. I've seen a couple of articles suggesting that it was becoming common in the USA for employers to ask for passwords, and I've seen a couple where legal and IT people have explained why this is a terrible idea, especially for the employer!
On a personal level, I have a facebook account. I have nothing there which I would be embarrassed about, bit I dio have things there which are private (pictures of my family, for instance) My privacy settings are high - you can't see my page unless I have friended you, and my profile picture is not of me, so unless you already know me elsewhere online (where I use the same picture) you won'tr know for sure it's me, and unless I know you, I won't freind you.
If an employer askes, then my first response would be to ask why they wished to know, and depending on heir reply, my next would be to tell them either that I have an account but it is kept provate and for family only, or (possibly) that I have an account but no longer use it (true, although not the whole truth. In addition to the account I use, I have a very old account. I cannot remember the password and no longer have the e-mail address it was linked to.
I might also explain that it breaches facebooks T&Cs to give your password to another person, so I won't be doing that.
As an employer, I google a prospective employee after the initial interview and before recalling them for a final interview or offering them a job. Ihave not yet had a situatio where what I founf caused me to reconsider hiring someone. What someone does in their own time is not my bisiness, but someone who has posts which were rude about their employer or clients, indiscreet about things which happened at work, or which showed that they had a habit of calling in sick after heavy nights out, or spending a lot of time on facebook or similar sites during working hours I would thinkl again.
If they have the common sense to keep their account locked, or accessible but discreet, then the rest iis none of my business.
If the question is geared to finding out whether an employee would be able to use social networking as part of their jobn I would be asking 'how familiar are you with facebook / twitter, not about their personal accounts.