Every state except Montana follows the basic premise that employees who don't have a written contract are "at will." That means you can fire them (and they can quit) for any reason or no reason, as long as its not illegal.
Every state recognizes at least one of the following exceptions to at-will employment:
Public policy exception
In more than 40 states you can't fire employees for reasons that violate an established public policy of the state.
Implied contract exception
In most states, courts may find you entered into an implied contract with employees by making certain promises to them – usually in your employee handbook. Your handbook or policies might contain promises to your employees that you’ll follow certain procedures before firing them. These assurances may create an implied contract with employees to do what you said you would do. In effect, that turns an at-will employee into a contractual one.
Also, an implied contract made have been made when you or a supervisor assured an employee that his job was secure. This and other similar statements could create an oral employment contract which a potential employee could sue to make enforceable. Finally, your initial letter offering the employee a job could be construed as an employment contract as well depending on the manner and structure of the letter.
Covenant of good faith and fair dealing
In fewer than 15 states, employers have a duty to act fairly and in good faith in all dealings with employees.
Related articles on Employment at Will from the State Employment Law Letters designates additional valuable resources available exclusively to Employment Law Letter subscribers