There are news stories surfacing today about job applicants being asked to supply Facebook login information to prospective employers, ostensibly to make sure the people they are hiring aren't making the mistake of having an actual personal life. Unless your family is living out of your car, and the only thing standing between them and a hot meal and a roof over their heads is your privacy, this is one area where you should stand your ground and refuse. Even if you've been living a squeaky-clean online social life, don't give in to the temptation to open your personal life to scrutiny from someone you don't know.
For one, if the employer has to rely on reading your private Facebook profile to determine whether or not to hire you, it's obvious hiring practices that have worked well for decades aren't being used properly, and you have to seriously question the competency of that company's leadership and recruiting team. No employer that I have ever worked for would even consider for a microsecond that this is an acceptable practice, and frankly, most HR managers still find the standard background check distasteful (but necessary) all on its own.
Secondly, regardless of how bad you want this job, do you really want to work for an employer to thinks it's OK to invade your personal life, especially one that may or may not hire you at all? Their willingness to even ask to see what you keep private means that they have no respect for your personal life, and you can bet this will extend to their practices in how they manage people who work for them.
Take a stand for your privacy. No job is worth sacrificing your personal life.