There are at least 57 different types of anarchism....
Here's how I break down what I consider the main trends in an 'introduction to anarchism' talk I do. Some of these still bear a close resemblance to the Wikipedia articles, etc. they were based on ;-)
Anarchist communism proposes that the freest form of social organisation would be a society composed of self-managing communes with collective use of the means of production, organised democratically and using consenus decision-making, and related to other communes through federation. In anarchist communism there would be no money but everyone would have free access to the resources and surplus of the commune. Anarchist communism is thus said to operate on a gift economy.
Collectivist anarchism is similar to anarchist communism, except for the fact that in collectivism workers would be compensated for their work on the basis of the amount of time they contributed to production, rather than goods being distributed "according to need" as in anarcho-communism. Some collectivist anarchists do not oppose the use of currency. Some support workers being paid based on the amount of time they contributed to production. These salaries would be used to purchase commodities in a communal market.
Syndicalism focuses on radical trade unions as a potential force for revolutionary social change, seeking to replace capitalism and the state with a new society that is democratically self-managed by the workers. Important principles of syndicalism include workers' solidarity, direct action (such as general strikes and workplace recuperations) and workers' self-management. Syndicalism is sometimes seen as simply a specific strategic focus within communist or collectivist anarchism as opposed to a distinct type of anarchism in itself.
On the other hand, Insurrectionary Anarchism opposes formal organizations such as labor unions and federations that are based on a political programme and periodic congresses. Instead, insurrectionary anarchists support informal organization and small affinity group based organization. Insurrectionary anarchists put value in attack, permanent class conflict, and a refusal to negotiate or compromise with class enemies.
Contemporary insurrectionary anarchism most often inherits the views and tactics of anti-organizational anarcho-communism.
Anarcha-feminism is a form of anarchism that synthesizes radical feminism and anarchism and views patriarchy (male domination over women) as a a form of. Anarcha-feminism was inspired in the late 19th century by the writings of early feminist anarchists such as Lucy Parsons, Emma Goldman and Voltairine de Cleyre. Anarcha-feminists, like other radical feminists, criticize and advocate the abolition of traditional conceptions of family, education and gender roles and believe that the feminist struggle against sexism and patriarchy is an essential component of the anarchist struggle. As Susan Brown puts it, "as anarchism is a political philosophy that opposes all relationships of power, it is inherently feminist".
Green anarchism (or eco-anarchism) is a school of thought within anarchism which puts an emphasis on environmental issues. Green anarchists often criticize the main currents of anarchism for their focus and debates about politics and economics instead of a focus on ecosystems.
Anarcho-primitivism is an anarchist critique of the origins and progress of civilization. According to anarcho-primitivism, the shift from hunter-gatherer to agricultural subsistence gave rise to social stratification, coercion, and alienation. Anarcho-primitivists advocate a return to non-"civilized" ways of life through deindustrialisation, abolition of the division of labour or specialization, and abandonment of large-scale organization technologies. There are other non-anarchist forms of primitivism, and not all primitivists point to the same phenomenon as the source of modern, civilized problems.
Primitivism is seem as extreme by some anarchists, but it does provide a useful counterbalance to the cheerful Industrial Revolution optimism expressed by the late 19th and early 20th Century anarchists like Peter Kropotkin that technology and technological progress are inherently liberatory and should be pursued by anarchists in a post-revolutionary society.
*****Post-structuralist anarchism / post-anarchism*****
The prefix "post-" does not mean 'after anarchism', but refers to the challenging and disruption of typically accepted assumptions within frameworks that emerged during the Enlightenment era. This means a basic rejection of some of the essentialist or reductionist notions of traditional anarchism. It argues that capitalism and the state are not the only sources of domination in the time in which we live, and that new approaches need to be developed to combat the network-type structures of domination that characterize late modernity.
*****Synthesism / anarchism without adjectives / Type-3 anarchism*****
Anarchism without adjectives is an attitude that tolerates the coexistence of different anarchist schools". Anarchism without adjectives emphasizes harmony between various anarchist factions and attempts to unite them around their shared anti-authoritarian beliefs. Rudolf Rocker said that the different types of anarchism presented "only different methods of economy, the practical possibilities of which have yet to be tested, and that the first objective is to secure the personal and social freedom of men no matter upon which economics basis this is to be accomplished."
It is important to note that a large number of self-defined anarchists might use more than one of these labels to describe themselves depending on what they were doing or what kinds of group structures they find themselves operating in: some anarchists prefer durable, structured groups where members commit to certain ideological and tactical principles; others prefer more flexible, small-scale affinity groups that come and go as needed. Often, members of these latter groups express concerns about how formal organisation can tend towards bureaucracy and the perpetuation of the life of the group for its own sake.
There are a number of other types of so-called anarchism that are problematic. Perhaps the worst of these is anarcho-capitalism - an oxy-moronic view stemming from the belief expressed by some so-called 'individualist anarchists' that personal freedom entails being free to compete in a capitalist-type market.