At-will employment is a term used in U.S. labor law for contractual relationships in which an employee can be dismissed by an employer for any reason (that is, without having to establish "just cause" for termination), and without warning. Questions using this tag should include the state/territory tag, not just the United States tag.
At-will employment is the default for all states in the U.S. except Montana.
There are several exceptions to at-will employment:
Statutory Exceptions. Federal and state laws that make certain causes for termination illegal (for example, discrimination).
Contracts. This includes both individual contracts and collective bargaining agreements. Most states also provide exceptions for implied contracts. (For example, an employer's policies regarding how employees are terminated might constitute an implied contract.)
Public Policy. You cannot be fired for refusing the break the law, reporting law breaking, exercising your rights, and performing civic duty. How this is interpreted varies by state.
Implied Covenant of Good Faith and Fair Dealing. A few states prohibit firing in bad faith. How this is interpreted varies by state.
Promissory Estoppel. Could be used in cases where an employee relied on a promise of employment and suffered damages when the offer was withdrawn. This varies by location.
Since the exceptions for at-will employment vary by location, questions using this tag should include the specific state/territory the OP resides in.
Sources and Additional Reading:
National Conference of State Legislatures - At-Will Employment - Overview
National Conference of State Legislatures - At-Will Employment Exceptions by State
U.S. Bureau of Labor Statistics - The employment-at-will doctrine: three major exceptions
AFL-CIO - Your Rights at Work - Terminated or Laid Off the Job
