Some people will argue for one, some for the other. I'd go with SSNs, as it's still perfectly clear what you're talking about. The basic rule about apostrophes is that they're used to indicate possession or to indicate contraction, not to pluralize.

But no one would crucify you if you went the other way, as it's also sometimes used to indicate pluralization of acronyms and abbreviations, and pretty much must be used when a simple trailing `s' is unclear.