A few days ago the Associated Press ran an article about one job applicant who was asked to provide their Facebook login and profile. The story then got a lot of legs getting including a local TV News from Fox-26TV here in Houston (video link below).
While private sector employers can certainly demand to see your profiles, provide passwords, etc., I would advise against it. In fact, there is risk in using the internet to screen applicants.
The short version is that you learn certain facts that are not supposed to be considered in the hiring process such as age, religion, family and marital status. You can’t unring that bell. So, if someone were to make a discrimination claim, you can argue you did not consider these factors, but there will be no question that you knew them when you made your decision.
I wrote a more detailed post here about the role of social media in the hiring process. I have a longer CLE paper on the topic, too. Send me an email if you would like the paper.