Yes. All branches of anarchism are opposed to capitalism. This is because capitalism is based upon oppression and exploitation (see sections B and C). Anarchists reject the "notion that men cannot work together unless they have a driving-master to take a percentage of their product" and think that in an anarchist society "the real workmen will make their own regulations, decide when and where and how things shall be done." By so doing workers would free themselves "from the terrible bondage of capitalism." 
(We must stress here that anarchists are opposed to all economic forms which are based on domination and exploitation, including feudalism, Soviet-style "socialism"—better called "state capitalism" --, slavery and so on. We concentrate on capitalism because that is what is dominating the world just now).
Individualists like Benjamin Tucker along with social anarchists like Proudhon and Bakunin proclaimed themselves "socialists." They did so because, as Kropotkin put it in his classic essay "Modern Science and Anarchism," "[s]o long as Socialism was understood in its wide, generic, and true sense -- as an effort to abolish the exploitation of Labour by Capital -- the Anarchists were marching hand-in-hands with the Socialists of that time."  Or, in Tucker's words, "the bottom claim of Socialism [is] that labour should be put in possession of its own," a claim that both "the two schools of Socialistic thought . . . State Socialism and Anarchism" agreed upon. Hence the word "socialist" was originally defined to include "all those who believed in the individual's right to possess what he or she produced."  This opposition to exploitation (or usury) is shared by all true anarchists and places them under the socialist banner.
For most socialists, "the only guarantee not to be robbed of the fruits of your labour is to possess the instruments of labour."  For this reason Proudhon, for example, supported workers' co-operatives, where "every individual employed in the association . . . has an undivided share in the property of the company" because by "participation in losses and gains . . . the collective force [i.e. surplus] ceases to be a source of profits for a small number of managers: it becomes the property of all workers."  Thus, in addition to desiring the end of exploitation of labour by capital, true socialists also desire a society within which the producers own and control the means of production (including, it should be stressed, those workplaces which supply services). The means by which the producers will do this is a moot point in anarchist and other socialist circles, but the desire remains a common one. Anarchists favour direct workers' control and either ownership by workers' associations or by the commune section A.3 on the different types of anarchists).
Moreover, anarchists also reject capitalism for being authoritarian as well as exploitative. Under capitalism, workers do not govern themselves during the production process nor have control over the product of their labour. Such a situation is hardly based on equal freedom for all, nor can it be non-exploitative, and is so opposed by anarchists. This perspective can best be found in the work of Proudhon's (who inspired both Tucker and Bakunin) where he argues that anarchism would see "[c]apitalistic and proprietary exploitation stopped everywhere [and] the wage system abolished" for "either the workman. . . will be simply the employee of the proprietor-capitalist-promoter; or he will participate . . . In the first case the workman is subordinated, exploited: his permanent condition is one of obedience. . . In the second case he resumes his dignity as a man and citizen. . . he forms part of the producing organisation, of which he was before but the slave . . . we need not hesitate, for we have no choice. . . it is necessary to form an ASSOCIATION among workers . . . because without that, they would remain related as subordinates and superiors, and there would ensue two. . . castes of masters and wage-workers, which is repugnant to a free and democratic society." [Op. Cit., p. 233 and pp. 215–216]
Therefore all anarchists are anti-capitalist ("If labour owned the wealth it produced, there would be no capitalism" [Alexander Berkman, What is Anarchism?, p. 44]). Benjamin Tucker, for example—the anarchist most influenced by liberalism (as we will discuss later) -- called his ideas "Anarchistic-Socialism" and denounced capitalism as a system based upon "the usurer, the receiver of interest, rent and profit." Tucker held that in an anarchist, non-capitalist, free-market society, capitalists will become redundant and exploitation of labour by capital would cease, since "labour. . . will. . . secure its natural wage, its entire product." [The Individualist Anarchists, p. 82 and p. 85] Such an economy will be based on mutual banking and the free exchange of products between co-operatives, artisans and peasants. For Tucker, and other Individualist anarchists, capitalism is not a true free market, being marked by various laws and monopolies which ensure that capitalists have the advantage over working people, so ensuring the latter's exploitation via profit, interest and rent section G for a fuller discussion). Even Max Stirner, the arch-egoist, had nothing but scorn for capitalist society and its various "spooks," which for him meant ideas that are treated as sacred or religious, such as private property, competition, division of labour, and so forth.
So anarchists consider themselves as socialists, but socialists of a specific kind -- libertarian socialists. As the individualist anarchist Joseph A. Labadie puts it (echoing both Tucker and Bakunin):
"It is said that Anarchism is not socialism. This is a mistake. Anarchism is voluntary Socialism. There are two kinds of Socialism, archistic and anarchistic, authoritarian and libertarian, state and free. Indeed, every proposition for social betterment is either to increase or decrease the powers of external wills and forces over the individual. As they increase they are archistic; as they decrease they are anarchistic." [Anarchism: What It Is and What It Is Not]
Labadie stated on many occasions that "all anarchists are socialists, but not all socialists are anarchists." Therefore, Daniel Guerin's comment that "Anarchism is really a synonym for socialism. The anarchist is primarily a socialist whose aim is to abolish the exploitation of man by man" is echoed throughout the history of the anarchist movement, be it the social or individualist wings. [Anarchism, p. 12] Indeed, the Haymarket Martyr Adolph Fischer used almost exactly the same words as Labadie to express the same fact -- "every anarchist is a socialist, but every socialist is not necessarily an anarchist"—while acknowledging that the movement was "divided into two factions; the communistic anarchists and the Proudhon or middle-class anarchists." [The Autobiographies of the Haymarket Martyrs, p. 81]
So while social and individualist anarchists do disagree on many issues—for example, whether a true, that is non-capitalist, free market would be the best means of maximising liberty—they agree that capitalism is to be opposed as exploitative and oppressive and that an anarchist society must, by definition, be based on associated, not wage, labour. Only associated labour will "decrease the powers of external wills and forces over the individual" during working hours and such self-management of work by those who do it is the core ideal of real socialism. This perspective can be seen when Joseph Labadie argued that the trade union was "the exemplification of gaining freedom by association" and that "[w]ithout his union, the workman is much more the slave of his employer than he is with it." [Different Phases of the Labour Question]
However, the meanings of words change over time. Today "socialism" almost always refers to state socialism, a system that all anarchists have opposed as a denial of freedom and genuine socialist ideals. All anarchists would agree with Noam Chomsky's statement on this issue:
"If the left is understood to include 'Bolshevism,' then I would flatly dissociate myself from the left. Lenin was one of the greatest enemies of socialism." 
Anarchism developed in constant opposition to the ideas of Marxism, social democracy and Leninism. Long before Lenin rose to power, Mikhail Bakunin warned the followers of Marx against the "Red bureaucracy" that would institute "the worst of all despotic governments" if Marx's state-socialist ideas were ever implemented. Indeed, the works of Stirner, Proudhon and especially Bakunin all predict the horror of state Socialism with great accuracy. In addition, the anarchists were among the first and most vocal critics and opposition to the Bolshevik regime in Russia.
Nevertheless, being socialists, anarchists do share some ideas with some Marxists (though none with Leninists). Both Bakunin and Tucker accepted Marx's analysis and critique of capitalism as well as his labour theory of value (see section C). Marx himself was heavily influenced by Max Stirner's book The Ego and Its Own, which contains a brilliant critique of what Marx called "vulgar" communism as well as state socialism. There have also been elements of the Marxist movement holding views very similar to social anarchism (particularly the anarcho-syndicalist branch of social anarchism) -- for example, Anton Pannekoek, Rosa Luxembourg, Paul Mattick and others, who are very far from Lenin. Karl Korsch and others wrote sympathetically of the anarchist revolution in Spain. There are many continuities from Marx to Lenin, but there are also continuities from Marx to more libertarian Marxists, who were harshly critical of Lenin and Bolshevism and whose ideas approximate anarchism's desire for the free association of equals.
Therefore anarchism is basically a form of socialism, one that stands in direct opposition to what is usually defined as "socialism" (i.e. state ownership and control). Instead of "central planning," which many people associate with the word "socialism," anarchists advocate free association and co-operation between individuals, workplaces and communities and so oppose "state" socialism as a form of state capitalism in which "[e]very man [and woman] will be a wage-receiver, and the State the only wage payer."  Thus anarchists reject Marxism (what most people think of as "socialism") as just "[t]he idea of the State as Capitalist, to which the Social-Democratic fraction of the great Socialist Party is now trying to reduce Socialism."  The anarchist objection to the identification of Marxism, "central planning" and State Socialism/Capitalism with socialism will be discussed in section H.
It is because of these differences with state socialists, and to reduce confusion, most anarchists just call themselves "anarchists," as it is taken for granted that anarchists are socialists. However, with the rise of the so-called "libertarian" right in the USA, some pro-capitalists have taken to calling themselves "anarchists" and that is why we have laboured the point somewhat here. Historically, and logically, anarchism implies anti-capitalism, i.e. socialism, which is something, we stress, that all anarchists have agreed upon (for a fuller discuss of why "anarcho"-capitalism is not anarchist see section F).
- Voltairine de Cleyre, "Anarchism", Exquisite Rebel, p. 75 and p. 79
- Evolution and Environment, p. 81
- The Anarchist Reader, p. 144
- Lance Klafta, "Ayn Rand and the Perversion of Libertarianism," in Anarchy: A Journal of Desire Armed, no. 34
- Peter Kropotkin, The Conquest of Bread, p. 145
- The General Idea of the Revolution, p. 222 and p. 223
- Marxism, Anarchism, and Alternative Futures, p. 779
- Benjamin Tucker, The Individualist Anarchists, p. 81
- Peter Kropotkin, The Great French Revolution, vol. 1, p. 31
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