Anarchism is not chaos; Anarchism is not rejection of organization. This is a popular misconception, repeated ad nauseam by the mass media and by anarchism's political foes. Even a brief look at the works of anarchism's leading theoreticians and writers confirms that this belief is in error. Over and over in the writings of Proudhon, Bakunin, Kropotkin, Rocker, Ward, Bookchin, et al., one finds not a rejection of organization, but rather a preoccupation with it—a preoccupation with how society should be organized in accord with the anarchist principles of individual freedom and social justice. For a century and a half now, anarchists have been arguing that coercive, hierarchical organization (as embodied in government and corporations) is not equivalent to organization per se (which they regard as necessary), and that coercive organization should be replaced by decentralized, nonhierarchical organization based on voluntary cooperation and mutual aid. This is hardly a rejection of organization.
Anarchism is not amoral egotism. As does any avant garde social movement, anarchism attracts more than its share of flakes, parasites, and outright sociopaths, persons simply looking for a glamorous label to cover their often-pathological selfishness, their disregard for the rights and dignity of others, and their pathetic desire to be the center of attention. These individuals tend to give anarchism a bad name, because even though they have very little in common with actual anarchists—that is, persons concerned with ethical behavior, social justice, and the rights of both themselves and others—they're often quite exhibitionistic, and their disreputable actions sometimes come into the public eye. To make matters worse, these exhibitionists sometimes publish their self-glorifying views and deliberately misidentify those views as "anarchist." The claim that amoral egotism—essentially "I'll do what I damn well please and <not allowed> everybody else" is absurd.
Anarchism is, in its narrowest sense, simply the rejection of the state... the rejection of coercive (read: violent) government.
The primary goal of anarchism is the greatest possible amount of freedom for all, anarchists insist on equal freedom in both its negative and positive aspects—that, in the negative sense, individuals be free to do whatever they wish as long as they do not harm or directly intrude upon others; and, in the positive sense, that all individuals have equal freedom to act, that they have equal access to the world's resources.
Anarchists recognize that absolute freedom is an impossibility, that amoral egotism, ignoring the rights of others would quickly devolve into a war of all against all. What we argue for is that everyone have equal freedom from restraint (limited only by respect for the rights of others) and that everyone have as nearly as possible equal access to resources, thus ensuring equal (or near-equal) freedom to act. This is anarchism in its theoretical sense.