These are important exceptions to termination for no reason under “employment at will.”
You may have a legal case if you can prove you were fired because of age, ethnic origin, race, religion, disability, gender, sexual harassment, sexual orientation, equal compensation, genetics, or pregnancy. This may also be true if you (or a family member) have a physical or mental disability or medical issues that were a reason for the termination.
You can get information on all of your rights and how to file a complaint by going to the website for the United States Equal Employment Opportunity Commission and reading "How to file a charge of employment discrimination." The law in this area is detailed and frequently changing, so it would be wise to consult an experienced employment lawyer.