Most of us who are not incorporated file taxes under our SSN. Problem is when people begin to ask you for this kind of info for paperwork. Since you're working as yourself, not a business, they are free to ask you for your SSN and you would legally have to provide it.
You can avoid this by doing a few of things which are very cheap:
* get yourself registered as a DBA (Doing Business As) so you're official (here in upstate NY, it cost me $25 to file a DBA with my county)
* get a sales tax number from your state agency (if applicable - should be free)
* go to the IRS website and apply for an EIN (Employer ID #) or TIN (tax payer ID #)(free)
With this, you will never have to give anyone you sell your services to your SSN. Instead you give them your EIN and if applicable, can charge them sales tax as a separate item, then pass it on to the state.
The key is being a DBA. You need to make the distinction between being their employee and being a company being contracted to do services for them. I get hired to do a shoot, they're hiring me via my DBA. I am not their employee and I will not be listed under their payroll in any way shape or form. If I did, my accountant would kick my butt into the next county