Short Answer: An employee may quit, or be fired, at any time with or without notice or cause.
Longer Answer (from http://www.ncsl.org/research/labor-and-employment/at-will-employment-overview.aspx):
"I. The At-Will Presumption
Employment relationships are presumed to be “at-will” in all U.S. states except Montana. The U.S. is one of a handful of countries where employment is predominantly at-will. Most countries throughout the world allow employers to dismiss employees only for cause.
A. At-Will Defined
At-will means that an employer can terminate an employee at any time for any reason, except an illegal one, or for no reason without incurring legal liability. Likewise, an employee is free to leave a job at any time for any or no reason with no adverse legal consequences.
At-will also means that an employer can change the terms of the employment relationship with no notice and no consequences. For example, an employer can alter wages, terminate benefits, or reduce paid time off. In its unadulterated form, the U.S. at-will rule leaves employees vulnerable to arbitrary and sudden dismissal, a limited or on-call work schedule depending on the employer’s needs, and unannounced cuts in pay and benefits.
B. Modification by Contract
The at-will presumption is a default rule that can be modified by [...]