The statusof a worker as an independent contractor or an employee is important for federal income and employment taxes (think IRS and Social Security Administration).
If you believe that you have been misclassified as an independent contractor, you can report it to the IRS using a form SS-8, Determination ofWorkerStatus for Purposes of Federal Employment Taxes and Income Tax Withholding (downloads as a pdf).
Even if the employer has a written agreement calling for the worker not to be an employee and agreeing to independent contractor status, the agency can rule for the worker, recharacterizing the relationship as that of employer-employee.