is a question you should not answer.
This is not a node about the right to privacy. I will presume you learnt the value of privacy the day your younger brother saw you wanking off to a dog-eared Playboy and ran over to tell your mom.
Amongst the few people you must disclose your SSN (Social Security Number) to are your employer, the Social Security Administration (SSA) and the Internal Revenue Service (IRS). Any government agency asking for your SSN must tell you whether there is a federal statute that makes your compliance mandatory, how your SSN will be used, and the consequences to you if you fail to provide your SSN. If there is no federal statute requiring you to disclose your SSN to this particular government agency, the Privacy Act of 1974 makes it illegal for any government agency to deny you a benefit or service based on your refusal to provide a SSN.
The SSN was created so the Social Security Administration could pay out Social Security benefits. That was its sole original intent. The federal government in 1936 assured the public SSNs would be used only by the SSA. Nowadays, if you are a US person you are required to report any income you receive to the IRS using a SSN. Since anyone who pays you monetary compensation is also required to disclose this income to the IRS, they need your SSN too. You could refuse to give your SSN to the IRS if you wish, the law mandating your disclosure is unclear. This would be rather quixotic and you could end up being subjected to IRS audits for the rest of your life. On the other hand, you might just become a defendant in a case before the Supreme Court and have first-year law students memorize your name forevermore.
There are no laws governing the use of your SSN by private organizations, the government assumes you are old enough to wipe your own ass. If you are asked for your SSN by a company you are doing business with, you are under no compulsion to disclose it. Private organizations use SSNs in different ways and various people may have access to the records, you should not assume the telephone company will guard your SSN as well as you might. Since your SSN has become a passphrase for credit in your name, you should think twice before you provide it to any old McCorp. If you are well informed, persistent and polite, the company you are dealing with will likely back down at some point and agree to use an alternative means of identification or authentication.