McAfee, the antivirus software company, recently released a list of the most dangerous places to give your Social Security number. Many of the places on the list might surprise you: 1. Universities and colleges. 2. Banking and financial institutions. 3.nd there are things you can do to detect identity theft and limit the damage. Donât be so quick to give out your number. As Levin said, a lot of organizations and companies will ask for your Social Security number.