The U.S. is an at-will country, which means an employer can usually let you go for almost any reason — or no reason at all — without notice. Montana is the lone holdout: under its Wrongful Discharge from Employment Act, employees there are entitled to "good cause" protection after a probationary period. Everywhere else, you start from at-will and look for an exception.
The exceptions cover a lot of ground. It's illegal to fire someone for a discriminatory reason (race, sex, age 40+, disability, religion, national origin, pregnancy), for reporting illegal activity, for exercising a legal right like filing a workers' comp claim or taking FMLA leave, or in violation of a written or implied employment contract. The pattern that wins these cases is timing — terminations that land 2 weeks after a complaint to HR or a doctor's note hitting management's desk look very different from a routine layoff.
If your firing fits one of these exceptions, the law calls it wrongful — and depending on the statute, you may be entitled to back pay, reinstatement, front pay, emotional distress damages, and attorney's fees.