It is a truism in Marxism that there is a formal legal equality in capitalism which masks a material inequality. The fiction is that workers and employers meet under equal terms in the marketplace as buyer and seller: seller of labor power as a commodity and buyer of labor power as a commodity. The material inequality behind the formal legal equality is the asymmetry of circumstances and consequences between the two. Quite simply, the results are get bad faster and are over all worse for workers should the exchange not take place. This is because the workers don’t have money. They sell labor power under compulsion, because there are only limited means to meet needs without money, and there are limited means to acquire money without the sale of one’s labor power as a commodity. 

This arrangement is enshrined in labor law in the United States, in the doctrine of "At-will employment."

The doctrine means "An employee is employed at the will of the employer for as little or as long as the private employer wishes, and in whatever lawful capacity the employer requires, "
and the "employer need not provide any reason for termination of an "at will" employee, so long as the termination isn’t unlawful or discriminatory (based on age, sex, national origin and disability)." (From an okay FAQ on rights re: job termination.)

Employment at-will "is the basic nature of the employment relationship for non-union, non-governmental, non-contractual employees: Employers can fire, discipline, or change the wages, shift, hours, jobs, etc. of any employee-at-will, for any reason or no reason, as long as their action does not violate some law" (Via), with a handful reasons which are illegal because they are considered discriminatory. (I don’t know when sex discrimination was added. My mom was fired from UPS for getting pregnant with me.) Even in cases of firing or changes for illegal reasons, the boss can deny that the firing is for that reason, claiming to be simply exercising the rights of an employer at-will. Proving otherwise is not easy, and even when successful it’s very slow. 

The effect of the doctrine in legal terms is succinctly summarized here: "As it pertains to private businesses and where there is no contract or collective bargaining agreement defining the work relationship, employers can establish almost any workplace rules they choose, unless restricted by other law."

Here is an example of a human resources policy spelling out at will status to employees:

"Employment with the company is "at-will." This means that you may terminate your employment at any time. It also means that the company can terminate your employment, at any time, with or without notice or cause. [Add if applicable: While the company generally adheres to progressive discipline, it is not bound or obligated to do so. Again, in the company’s sole discretion, you may be terminated at any time, with or without notice or cause].

As an at will-employee, you are not guaranteed, in any manner, that you will be employed for any set period of time. No one in the company, except the President, in a written, signed contract, may make any representation or promise to you that you are other than an at-will employee. Any employee, manager or supervisor who makes such a representation or promise to you is not authorized to do so."

This site has a lot of information on the idea of at-will employment and its history. Here is an example of a defense of at-will employment, about which I have nothing to say that one puts on websites.

One important category which is protected, such that the employer can not legally fire workers for this reason, is concerted activity. Concerted activity is when a group of workers collectively approach the boss demanding changes at work. (See here and here.) It is a right covered under the National Labor Relations Act, which is worth a read in its entirety as is this excerpt from the original Wagner Act and comments by people on the left at the time of the Act’s writing, opposing the Act. (I’ve written about some of this before.) The Act is administered by the National Labor Relations Board. The NLRB’s powers are weak, and it’s active oversight and enforcement of the law being followed or not is poor. It’s only gotten worse under the Bush administration, having issued rulings like the one which decided that graduate employees at private universities have no rights to organize.

The NLRB process has never been good to make strategic use of, that’s why it exists. It can, however, be used tactically - exclusively defensively - for good effect, particularly if there’s a good organizational plan. (I got 3 grand in back wages once via that process. That wasn’t good enough by a mile, but was still a far cry from nothing at all.) Reliance upon the NLRB is part of makes the business unions problematic, though only part. The inadequacy of the NLRB also makes alternative organizational models an important avenue of research, such as UE Local 150’s campaign in North Carolina.

All of this is also a factor in precarity in the United States, which is quite old.