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From the Social Security Administration's web site
Giving Your Number To Others
If a business or other enterprise asks you for your Social Security number, you can refuse to give it to them. However, that may mean doing without the purchase or service for which your number was requested. For example, utility companies and other services ask for your Social Security number, but do not need it; they can do a credit check or identify their customers by alternative means.
Giving your number is voluntary even when you are asked for the number directly. If requested, you should ask:
The answers to these questions can help you decide if you want to give your Social Security number. The decision is yours.
Our primary message is this--be careful with your Social Security number and your card to prevent their misuse.
From the Federal Trade Commission's web site
Give your SSN only when absolutely necessary. Ask to use other types of identifiers when possible. If your state uses your SSN as your driver’s license number, ask to substitute another number.
A Special Word About Social Security Numbers
Your employer and financial institution will likely need your SSN for wage and tax reporting purposes. Other businesses may ask you for your SSN to do a credit check, like when you apply for a loan, rent an apartment, or sign up for utilities. Sometimes, however, they simply want your SSN for general record keeping. You don’t have to give a business your SSN just because they ask for it. If someone asks for your SSN, ask the following questions:
Sometimes a business may not provide you with the service or benefit you’re seeking if you don’t provide your SSN. Getting answers to these questions will help you decide whether you want to share your SSN with the business. Remember – the decision is yours.