Even with the rise in identity theft, many places ask for your social security number and personal information that they don't actually need for you to do business with them. Take a look at the Adam Levin report on Identity Theft and how to protect yourself.
Poor Mrs. Hilda Schrader Whitcher had a copy of her social security card put in every wallet her employer sold in 1938!
Tips to protect your social security number
Always ask why they need your number and if it will be protected or shared. Many places, especially doctor's offices, want you to sign a form saying you have received their privacy policy but don't give you one. Always insist on it. Don't ever sign something saying you've received a form that they haven't given you.