The information, such as Social Security Number (SSN) or Employer Identification Number (EIN), is needed when filing 1099's to the federal agency. This is also in compliance with the IRS guidelines for 1099's.
QuickBooks will not allow to file 1099 without SSN. You have to ask this number to your contractors. However, if your contractors doesn't have SSN number, I'd suggest contacting IRS. They can give you advice and more details on what to do if the contractors doesn't have SSN number.