For my job I was required to undergo a background check, a credit check, and a drug test. Had to provide SS# along witih driver's license and complete employment timeline. For the record I was going thru this for an insurance job. I'm pretty sure that most places that have a sizeable number of employees perform checks on them of some sort or another--and you need the SS for that. I can tell you this: there are some places that don't consider this a good identifier anymore if you're trying to verify someone's identity over the phone because the SS is too widely available and too easy for someone else to get and use.
Sometimes it is a conundrum.