I just had quite a few recruiters call me this afternoon about the same job. This job appeared nice, but near the end of the conversation, the recruiter said "I need your SSN to submit this job application". Immediately, out of reflex, I said I'm not providing my SSN over the phone. I had to go into a very lengthy discussion with one of the recruiters on why I feel the way I do. He took it as a personal attack against his character. After I got it into his head that I didn't have a problem with him, or his recruiting company, or the company I would be applying to, but with the actual process of delivering my SSN over the phone, I think it sunk in.
While I realize your SSN is not the sacred jewels anymore and they are all probably out there anyway, why excite the matter? I've dealt with plenty of recruiters and applied for many jobs, many of whom require a SSN on the application. The difference here is a company who requires a SSN on the application now takes responsibility for that information, they are not a 3rd party like the recruiter is. While I don't agree with submitting a SSN even on a company application, it is a standard and flawed pre-hire process.