The Baltimore Sun Consuming Interests blog posted a great explanation  about when you actually have to provide your Social Security number.

Some of the most common instances include when you open bank accounts or apply for a new job.  You may need to provide a leasing office with my social security number so they could run a credit check before you are approved to live there. That’s fairly common too. There are lots of other circumstances when you may need to provide your Social Security number, and you can learn how companies and organizations use it.The Social Security Administration identified a few instances when legally you must provide your number.

If you’re uncomfortable with giving out your social security number, the Sun recommended asking the company what they need it for and if there is some alternative form of identification you can give. If there’s not, ask about how the company will protect your identity.