Most CUSIP numbers are for mutal funds and bonds and things of that nature. CUSIP are identification numbers assigned to all stocks and registered bonds. It stands for The Committee on Uniform Securities Identification Procedures (CUSIP) and these *people* oversee the entire CUSIP system.
It is used mainly in the USA and in Canada - Foreign Securities have a similar number called CINS number.
So - no, your SSN doesn't *really* have a CUSIP # although it would be *associated with one if you have bonds. :} Hope that answers your question and thanks for asking!
Also - this link might help.