No one needs it except the payroll office, which is not a consideration at the audition. You are there to read from the script, improvise and make the determination if you are right for the role. If anyone asks for your social security number, politely decline. If there is a paycheck involved and taxes are to be taken out, then the payroll company will get your social security number when you fill out your tax deduction payroll forms. Crooks and deceivers, or those with questionable ethics could make a lot of money from auditioning people with no intention of making a movie.
Auditions are part of a job application process.
We have laws to protect employers from such practice. Do not confuse this with standard registration fees collected by casting directors. It shouldn't ever be more than that to register with a casting director, and it's usually worth that investment. There is the potential that the footage could end up on the Internet, or anywhere else for that matter, in questionable circumstances. Face it, if your film director hasn't been to film school, or doesn't come from a theatre background, just bought a DV camera and needs to find some actors, he or she may not know what standard practices are.