ACCESS U.S. SOCIAL SECURITY WEBSITE
They allow it. Employers can verify up to 10 Social Security numbers. You can also do bulk verification through the website.
REGISTER
For the entire country's safety, anyone who wishes to utilize this feature is required to register in the website. The direct link for the registration is www.ssa.gov/bso/bsowelcome.htm
REQUEST ACTIVATION
After requesting for activation, wait for access codes to be mailed which you can then use in the website. Take note that there is expiration for your access. Use it while you can to avoid having to register again.
OTHER TRACKING WEBSITES
There are other private websites that can do a free lookup for you (but for more background data you'll have to invest some money.) US Search is one of the best I've seen. You have the link to their website on this page below "Resources."
There are also some other companies too but for individuals then best is US Search. If you're an employer and you want to do free SSN lookup or validation then you should consult authorities and private investigation boards for recommendations.