Most states are employment-at-will states which means the employer may terminate any employee at any time, for any reason, or for no reason. As a general rule, therefore, the employee has no right to challenge the termination. There are a few very limited exceptions. Also, federal law protects employees from discrimination because of age, race, sex, religion, national origin or handicap.
http://en.m.wikipedia.org/wiki/At-will_employment