Because a number of people have been asking (including the folks at Bureaucrash) I've developed a basic history of anarchism in the form, more or less, of a reading list.
Anarchist Political Theory: a Reading Guide
In my view, anti-authoritarianism and scepticism about state power are as old as authority and the state. Many of its expressions have certainly been repressed. In ancient Chinese philosophy, Taosim can be considered an anarchist political philosophy. The Tao Te Ching (circa 450 BC) is a surprisingly political text, often pretty direct in its anarchism. The Chuang Tzu, perhaps even a greater book, likewise. You want Burton Watson's complete translation of the text, and not just the "inner chapters."
An obviously anti-authoritarian tradition in ancient Greece is Cynicism, and Diogenes famously told Alexander the Great to get out of his face. One might try Luis Navia's book Diogenes the Cynic.
In my view, modern anarchism begins as a religious tradition associated with radical elements of the Protestant Reformation. The attack on the institutional power of the Church and the defense of individual conscience as an ultimate religious arbiter were quickly extended to an attack on the institution of the state and a defense of the individual conscience as the ultimate moral arbiter. One might consider here the notion of "inner light" in Quakerism, but more clearly in Anabaptist and other pietist sects. Also in the "antinomianism" of figures such as Anne Hutchinson. The Cambridge reader The Radical Reformation is a good place to begin.
Often an anthology of anarchist political theory will begin with William Godwin, a shockingly good and undervalued political philosopher, in the late eighteenth century. Godwin was the husband of ur-feminist Mary Wollstonecraft, the father of Mary Shelley, and hence the father-in-law of Percy Shelley. His classic An Enquiry Concerning Political Justice (1793) is, incomprehensibly, out of print. The best option is probably Peter Marshall's The Anarchist Writings of William Godwin. Godwin's anarchism is eminently rational, with a utilitarian ethical orientation.
Because government rests on force, pacifism entails anarchism, though not all pacifists have seen this connection. But expressions of this can be found in, for example, the writings of American religious pacifists such as David Low Dodge (see especially the second item on that link: "The Mediator's Kingdom" (1809)) and Adin Ballou, for example in Christian Non-Resistance. Leo Tolstoy also drew these implications in The Kingdom of God is Within You and other writings. Related versions of Christian anarchism and pacifism were developed by the great abolitionist William Lloyd Garrison and Nathaniel Rogers.
American utopians, individualists, and transcendentalists of the nineteenth century developed an elaborate philosophical and practical anarchist program. I might mention Thoreau's "Civil Disobedience" of 1848 and Emerson's great essay "Politics" of 1844. Some of the wildest and at the same time most practical metaphysical and economic theories of individualist anarchism were developed by Josiah Warren, who also edited what might be the first anarchist periodical, The Peaceful Revolutionist, in the 1830s. Connected developments might be associated with William Batchelder Greene, who developed a system of mutual banking. Lysander Spooner was a brilliant abolitionist, expert on legal history, and systematic theorist of individualist anarchism. The astounding American essayist Voltairine de Cleyre, though emerging later, comes from this tradition. I'd of course recommend the book I co-edited: Exquisite Rebel.
"Egoism" is an extreme version of individualist anarchism invented by the "left Hegelian" and opponent of Marx Max Stirner. His book The Ego and Its Own (1844) is quite something, a kind of pre-Nietzschean masterpiece. Stirner's egoism was later elaborated and connected to the American individualist tradition by Ben Tucker.
Pierre-Joseph Proudhon was probably the first theorist to call himself an anarchist, and was an early leftist opponent of Marx (on the grounds of Marx's totalitarianism). By far the most accessible work in English is What is Property? (1840), perhaps not his best or most important work. Shawn Wilbur is working on this problem. Proudhon's position is often called "mutualism" (also, "federalism") and is interesting in relation both the individualist and communist anarchism.
Communist anarchism was both influenced by and developed in opposition to Marx. It emerged as a critique of property and industrial capitalism (whereas individualist anarchism emerged from early nineteenth-century reform movements, often religious), and provided the main alternative to Marxist communism in the liberation movements of the late nineteenth and early twentieth centuries. In common with Marxism, it is often fundamentally materialist in its metaphysics, and analyzes human society in terms of class structure. It differs in prescribing non-state or non-coercive solutions. Mikhail Bakunin was an important organizer, and helped inject atheism into the whole deal, but was not, if you ask me, a particularly impressive thinker; certainly he pales in comparison to his rival Marx. The best and most systematic and influential theorist of communist anarchism was the Russian prince and scientist Peter Kropotkin. His anti social-Darwinist views on evolution, expressed in Mutual Aid (1902), are classic. The Italian Errico Malatesta should also be mentioned. The Russian-American anarchists Emma Goldman and Alexander Berkman were essentially followers of Kropotkin, but made independent contributions. Goldman's collection of essays Anarchism was what originally converted me, and Berkman's ABC of Communist Anarchism and Prison Memoirs of an Anarchist (1912) (he was jailed after he shot the industrialist Henry Clay Frick) are excellent.
Bringing the thing closer to now, one might mention in an individualist vein figures such as Murray Rothbard and the fascinating Karl Hess, who wrote speeches for Barry Goldwater. In a communist-style vein, there is of course Noam Chomsky.
Postmodernism has displayed various anarchist tendencies. I might mention Michel Foucault's brilliant and fundamental Discipline and Punish (1975), which describes the birth of the modern prison and modern "carceral" society, and the astonishing TAZ (Temporary Autonomous Zone) (1985) by Hakim Bey (Peter Lamborn Wilson).
Contemporary anti-globalization, anti-capitalist, squatter, and anti-intellectual property folk often refer to themselves as anarchists.
The best overall history is Peter Marshall's excellent Demanding the Impossible.