Definitions
Anarchism: the political philosophy according to which all human associations ought to be fully voluntary.
Coercion: limitation of a choice situation faced by a person P by the intentional act of Q, for Q's purposes; typically constraint to a certain course of action by increasing the costs of the alternatives.
Voluntary: uncoerced.
Political freedom or liberty: the condition of a life over a segment of time in which one is not subject to coercion by government, or is subject to coercion by government only to some limited extent.
Government: a group of people who claim and to an effective extent exercise a monopoly of coercion, resting on deadly force, over a definite geographical area, and the artifacts and procedures by which they do so.
State: the corporate agent of the acts of a government; the representation of a government as a singular actor.
Legitimacy: the quality of a state in virtue of which its coercive force is morally justifiable, or in which its laws impose prima facie duties.
Sovereignty: legitimate governing power; the control over territory by a legitimate government.
Varieties of Anarchism
Ancient
Cynicism a la Diogenes involves the complete negation of human authority; Diogenes is pictured as treating Alexander the Great with consummate disrespect. The ancient Stoics also tended to replace government authority with self-discipline. Rejection of pretensions to run the lives of other people - as well as a refusal to be run - is fundamental to Taoism.
Lao Tzu (7th c. BCE?)
Diogenes of Sinope (4th c. BCE)
"Without Adjectives"
William Godwin (British, 1756-1836)
Voltairine de Cleyre (American, 1866-1912) [voltairine.org/index.html]
Religious
There have been anarchists whose basic orientation has been provided by many different relgions. One important strand is radical Protestantism, which emphasizes "the priesthood of all believers" (Luther): the idea that it is wrong for a hierarchy to stand between each person and God, and that God speaks to us morally through the individual conscience, not the state's laws. This strain of anarchist thought has often been associated with pacifism.
radical Anabaptists (German etc: 16th century on)
Diggers, Ranters (British, 17th century)
William Lloyd Garrison (American, 1805-1879)
Leo Tolstoy (Russian, 1828-1910)
Dorothy Day (American, 1897-1980)
Individualist
What I'm calling "individualist" anarchism is characterized by the assertion that each person is owner of herself or is self-sovereign, while also emphasizing the connections of individuals to one another and to the world. A classic statement is Thoreau's "Civil Disobedience" which treats government authority as having no authority over individual conscience. These figures affirm private property, but tend to reject profit-driven capitalism.
Nathaniel Rogers (American 1794-1847) [crispinsartwell.com/rogershome.htm]
Josiah Warren (American, 1798-1874) [crispinsartwell.com/josiahwarren.htm]
Henry David Thoreau (American, 1817-1862)
Ralph Waldo Emerson (?) (American, 1803-1882)
Lysander Spooner (American, 1808-1887) [lysanderspooner.org]
Mutualist [mutualist.blogspot.com/]
[libertarian-labyrinth.blogspot.com/]
Mutualism emphasizes cooperative, local economic organizations, such as trade guilds and mutual banks, as the basic political units. (It's sometimes called "federalism.") Proudhon was probably the first thinker to call himself an "anarchist." It is compatible with individualist anarchism.
Pierre-Joseph Proudhon (French, 1809-1865)
William B. Greene (American, 1797-1877)
Egoist
Egoism might be termed extreme individualism. At times coming close to solipsism, it makes individual perception the ultimate criterion of morality and truth. It also tends to regard all human action as self-interested.
Max Stirner (German, 1806-1856)
Benjamin Tucker (American, 1854-1939)
Communist
Influenced by Marx's view of history as class struggle and his condemnation of industrial capitalism, communist anarchists attacked the authoritarian tendencies of Marxist communism. They held it likely that after the elimination of the state, land and other resources and capital (the means of production) would be communally held rather than privately owned. Syndicalism emphasizes labor union organizing.
Mikhail Bakunin (Russian, 1814-1876)
Peter Kropotkin (Russian, 1842-1921)
Emma Goldman (Russian/American, 1869-1940)
Noam Chomsky (American, 1928- )
Capitalist (libertarianism)
Anarcho-capitalism combines egoism with a laissez-faire economic scheme. Ayn Rand's notion of the strong, independent individual and the "virtue of selfishness" have been extremely influential.
Ayn Rand (?) (Russian/American, 1909-1962)
Murray Rothbard (American, 1926-1995)
"Minarchism"
Minarchists are capitalist individualists who assert the legitimacy only of some very minimal state power or enforcement association to defend individual rights defined by contract.
F.A. Hayek (1899-1992)
Robert Nozick (1932-2002)
Primitivist
Anarcho-primitivism at its most extreme (in Zerzan) holds that everything went radically wrong with the invention of agriculture and the alphabet. Jensen's is a milder variety, pointing to the totalitarian effects of many technologies. Anarcho-primitivism has provided some of the theoretical underpinnings of the anti-globalization movement.
John Zerzan (American, 1943- )
Derrick Jensen (American)
Post-structuralist
Many post-structuralist and postmodern philosophers have followed Foucault in developing an elaborate critique of the power of institutions, and Deleuze in celebrating movements of escape and pockets of resistance. Bey's notion of the Temporary Autonomous Zone (TAZ), particularly as an aspect of the internet, has been influential.
Michel Foucault (French, 1926-84)
Gilles Deleuze (French, 1925-1995)
Guy Debord (and situationism) (French, 1931-1994)
Hakim Bey (Peter Lamborn Wilson) (American) [www.hermetic.com/bey/taz_cont.html]
I aspire to an anarchism that
(1) rests on the idea that each person is the owner of herself or is self-sovereign;
(2) takes the individual human body to be the primary location of consciousness, identity, decision, and responsibility;
(3) is fundamentally "nominalist" with regard to collective entities such as peoples, classes, nations, institutions, families and so on: seeks to explain the action of such entities by appeal to states and transformations of the individuals out of which they are composed;
(4) does not regard human beings as merely self-interested or incapable of altruism;
(5) does not regard human beings exclusively in their economic aspect and does not seek to reduce human action to a single dimension of causation but to recognize a plurality of personalities and motives;
(6) emphasizes the connection of the individual to other persons as constitutive of individuality, but asserts that an affirmation of individuality is the first moment in re-establishing this connection;
(7) emphasizes the connection of the individual to the order of nature and its constitution out of such relations;
(8) is not an amoralism or an immoralism or a libertinism but an assertion of conscience and self-discipline;
(9) does not prescribe any particular set of social arrangements but leaves such arrangements to the voluntary decisions of individuals.