Aren't statists terrorists? Well, some of the them are; in fact, the overwhelming majority of non-governmental groups who murder and destroy property for political aims believe that government ought to exist (and that they ought to run it). And just as the existence of such statist terrorists is a poor argument for anarchism, the existence of anarchist terrorists is a poor argument against anarchism. For any idea whatever, there will always be those who advocate advancing it by violence.
It is however true that around the turn of the century, a certain segment of anarchists advocated what they called "propaganda by the deed." Several heads of state were assassinated by anarchists, along with businessmen, industrialists, stock-brokers, and so on. One of the most famous instances was when the young Alexander Berkman tried to murder the steel industrialist Henry Frick. During this era, the left-anarchists were divided as to the permissibility of terrorism; but of course many strongly opposed it. And individualist anarchists such as Benjamin Tucker almost always saw terrorist activities as both counter-productive and immoral when innocents were injured (as they often were).
The basic argument of the advocates of "propaganda by the deed" was that anarchist terrorism would provoke governments — even avowedly liberal and democratic governments — to resort to increasingly harsh measures to restore order. As governments' ruthlessness increased, their "true colours" would appear for all to see, leading to more immediate results than mere education and theorising. As E.V. Zenker notes in his Anarchism: A Criticism and History of the Anarchist Theory, a number of Western governments were driven to adopt anti-terrorist laws as a result of anarchist terrorism. (Zenker goes on to note that Great Britain remained true to its liberal heritage by refusing to punish individuals merely for espousing anarchist ideas.) But as one might expect, contrary to the terrorists' hopes, it was the reputation of anarchism — peaceful and violent alike — which suffered rather than the reputation of the state.
Undoubtedly the most famous modern terrorist in the tradition of "propaganda by the deed" is the so-called Unabomber, who explicitly labels himself an anarchist in his now-famous manifesto. In his manifesto, the Unabomber makes relatively little attempt to link himself to any particular figures in the anarchist tradition, but professes familiarity and general agreement with the anarchistic wing of the radical environmentalist movement. A large proportion of this wide-ranging manifesto criticises environmentalists' cooperation with socialists, minority rights activists, and other broadly left-wing groups; the point of this criticism is not of course to propose an alliance with conservatives, but to reject alliance with people who fail to reject technology as such. The more positive portion of the manifesto argues that freedom and technology are inherently incompatible, and outlines a program for the destruction of both modern industry and the scientific knowledge necessary to sustain it.
The large majority of anarchists — especially in modern times — fervently oppose the killing of innocents on purely moral grounds (just as most non-anarchists presumably do, though anarchists would often classify those killed in war as murder victims of the state). Nonviolence and pacifism now inspire far more anarchist thinkers than visions of random terror. Anarchists from many different perspectives have been inspired by the writings of the sixteenth-century Frenchman Etienne de la Boetie, whose quasi-anarchistic The Discourse of Voluntary Servitude spelled out a detailed theory of nonviolent revolution. La Boetie explained that since governments depend upon the widespread belief in their legitimacy in order to rule, despotism could be peacefully overthrown by refusing to cooperate with the state. Henry David Thoreau influenced many nonviolent protest movements with a similar theme in "On the Duty of Civil Disobedience." As Thoreau put it: "If the alternative is to keep all just men in prison, or give up war and slavery, the State will not hesitate which to choose." The success of the nonviolent anti-communist revolutions lends new support to the tactical insight of la Boetie and Thoreau.
But anarchists have a more instrumental reason to oppose the use of violence. Terrorism has been very effective in establishing new and more oppressive regimes; but it is nearly impossible to find any instance where terrorism led to greater freedom. For the natural instinct of the populace is to rally to support its government when terrorism is on the rise; so terrorism normally leads to greater brutality and tighter regulation by the existing state. And when terrorism succeeds in destroying an existing government, it merely creates a power vacuum without fundamentally changing anyone's mind about the nature of power. The predictable result is that a new state, worse than its predecessor, will swiftly appear to fill the void. Thus, the importance of using nonviolent tactics to advance anarchist ideas is hard to overstate.