Personally, I do not provide my SSN in most cases where it is requested. I usually ask why they want it and then decline.
The explanation may be perfectly logical (e.g. if there were financial responsibility in the role and they wanted to run your credit), but the appropriate time for something like this would be after the initial qualification. (All employers, obviously, will eventually need your SSN to report your income to the IRS.)
A move like this is reasonable to interpret as a signal of the kind of company you'd be working for if you joined -- placing their process above your personal privacy. In my experience, the UX of the hiring process has almost always been a very strong indicator of the company UX.
... This is totally logical but I still would never answer it personally. I almost never answer questions that make me uncomfortable during a hiring process and have never been dinged for it AFAIK. I guess everyone has their own thresholds.
Quantity of bureaucracy is my heuristic for how normal it is to ask this question, though this can vary.
Even if it's a job that requires a background/credit check, then they should (at the end of the process) make an offer contingent on passing the credit check.
Don't give out your SSN until you're at the offer stage.
http://www.realfreemarket.org/blog/2012/05/24/headhunters-de...