Sheri Berman in Dissent:
What are the uses of anarchism? The short answer is “not many.” Although anarchists have often been motivated by worthy aspirations and occasionally raised awareness of crucial issues, in general, anarchism is an ineffective way of improving the world. Anarchists are better dreamers than doers, and politics is the art of the possible. Although it may disappoint many on the left, a successful movement requires compromise, organization, and yes, even leadership, to actually get things done.
There are many variants and historical manifestations of anarchism, but characterizing all is a rejection of authority and hierarchy. Anarchists dream of a world without states, traditional political organizations, or any other structures that restrict individual freedom. Because they share such beliefs and goals with libertarians, anarchists are easily confused with them. In the American context, at least, the main distinction between the two concerns capitalism: anarchists view it as inherently coercive, while libertarians venerate it as the embodiment and guardian of individual rights. This has led the former to be viewed as left wing and the latter as right wing, but in reality, anarchists differ dramatically from other sectors of the modern left (just as libertarians differ dramatically from traditional conservatives and other factions of the modern right).
During the late nineteenth and early twentieth century anarchism’s rejection of traditional political organizations and activity led to its involvement in various uprisings and rebellions, the most important of which was the Paris Commune. Anarchists also became associated with “propaganda of the deed”—“spontaneous” and “voluntary” actions that reflected the power of the individual and were designed to inspire others. Although these actions need not necessarily be violent, they often were: during this period anarchists were responsible for a series of spectacular assassinations and bombings. A czar of Russia, presidents of Italy and France, kings of Portugal and Greece, and a president of the United States all met their ends at the hands of anarchists. Despite their often spectacular nature, anarchist activities were almost uniformly unsuccessful.
More here. See Marina Sitrin's counterargument here.