I get inquiries from job seekers quite frequently who are concerned about providing their social security number when they complete job applications. State laws vary on what information can be collected from applicants and most states don't prohibit companies from asking for social security numbers.
Some employers (including state hiring agencies) require applicants to list their social security number when completing job applications. If you don't list it, your application may not be considered. However, if you can avoid listing it until you are actually considered for the job, it makes sense to keep your social security number and other personal information confidential, if at all possible, until you are further along in the hiring process.
Scammers often ask for social security numbers as part of a fake job application or as part of the hiring process for a job that doesn't exist.
In addition, definitely do not email your social security number to any prospective employer - or to anyone, in general. I've actually received email job applications (even though I am not hiring) that included a social security number, along with additional personal information marital status, home address and phone number.
Before you give out your social security number, you need to be really careful about who you give it to and under what circumstances you disclose it. The Privacy Rights Clearing House has advice on how to careful check out companies who request it and what you can do to protect your social security number online.
Here's more information on whether employers can ask for your social security number.
More Information: Privacy Rights Clearing House - My Social Security Number