Most employees work at will, which means they can quit at any time, and can be fired at any time, for any reason that is not illegal. (It's illegal to fire even an at-will employee for discriminatory reasons or to retaliate against the employee for filing a complaint, for example.) At-will employment doesn't just cover firing, however: An employer can also change the status of an at-will employee -- including, for example, the employee's hours, salary, title, job duties, worksite, and so on -- without notice and without cause.
Most employees in the United States work at will. In every state but Montana (which protects employees who have completed an initial probationary period from being fired without cause), employers are free to adopt at-will policies -- and many have. Even if your employer doesn't have an at-will policy, the law presumes that employees work at will unless they have an employment contract that says otherwise, or their employer has given some clear indication that it will fire employees only for cause.
If you have an employment contract that limits the reasons for which you can be fired or sets the terms of your employment, your employer must abide by the agreement. For example, if you have a two-year contract that sets out your salary, bonus schedule, position, and job duties, those terms can't be changed while the contract is in effect. The contract is a legal agreement that both you and the employer have to honor; to change its terms, you have to negotiate a new agreement.
Contracts don't have to be in writing. If your employer has explicitly promised that it won't change certain terms of your employment or won't fire you without cause, that's an oral contract. For example, if your manager stated, during a job interview, that you would be given at least a year to prove yourself, and that all employees earn a minimum base salary orf $3,000 per month, you may be able to enforce those statements as an oral contract. If your base salary were changed, or you were let go during your first year, you may have a breach of contract claim.
Some contracts are neither in writing nor stated explicitly, but are instead implied from all of the circumstances. For example, if the employee handbook sets out a pay schedule and states that employees may be fired only for a specified list of reasons, that could create an implied contract. An employer that deviates from the promises in its handbook and policies may be legally liable.
If you're employed at will, your employer doesn't just have the right to fire you without notice or cause. It can also modify the terms and conditions of your employment without notice or cause. For example, an employer could demote you, change your pay structure, cut your pay, cut your hours, change your schedule, change your job responsibilities, change your reporting relationships, require you to work at another site, and so on. Of course, you are free to quit and look for other work if you don't like these changes. But your employer is free to make them without running afoul of the law, unless the employee is acting for illegal reasons.
For example, even at-will employees are protected from retaliation for reporting discrimination, harassment, unsafe working conditions, and so on. If you complained of sexual harassment, and your employer responded by demoting you, that would not be legal. Even though your employer has the right to demote you generally, it does not have the right to demote you for illegal reasons.
As you can see, even at-will employees have certain rights, including the right not to be subjected to illegal working conditions. If your employer disciplines, fires, or takes other negative actions against you because you have exercised a legal right or refused to do something illegal, you should consider a consultation with an employment attorney.