I'd just like to point out that the OP is not talking about faking an SSN. He's talking about communicating to the company that he has no intention of sharing his SSN by putting in a string of zeroes.
My parents, because they're backwards-ass paranoid militia people, do the same thing constantly, and they've never been called on it.
That said, let me enlighten you on the law:
1) It's not illegal for a company to request your SSN.
2) It's not illegal for you to refuse to supply it. Exception: SSN required by federal law.
Federal law requires private businesses to collect your SSN when (1) you are involved in a transaction in which the Internal Revenue Service requires notification, or (2) you are engaged in a financial transaction subject to federal Customer Identification Program rules.
3) It's not illegal for the business to tell you to stuff it and refuse to do business with you until you supply it.
But, in the interest of their bottom line, most businesses are willing to use all-zeroes or all-nines in their records, as a placeholder that says "is paranoid. don't ask." to anyone who sees it.
That said, if you're getting paid more than a very limited amount each year by a given company, it certainly falls under the "IRS requires notification" category.
