Political theory opposed to all forms of government.
Anarchists believe that the highest attainment of humanity is the freedom of the individual to express himself, unhindered by any form of repression or control from without.
The belief that all governments rest on violence to control their subjects.
Source: 1984 Funk & Wagnalls Encyclopedia
--> See Anarchy
"Anarchism does not mean bloodshed; it does not mean robbery, arson, etc. These monstrosities are, on the contrary, the characteristic features of capitalism. Anarchism means peace and tranquility to all." --August Spies, Haymarket anarchist
Britannica Definition (excerpts)
ANARCHISM (from the Gr. av, and aoxn, contrary to authority), the name given to a principle or theory of life and conduct under which society is conceived without government - harmony in such a society being obtained, not by submission to law, or by obedience to any authority, but by free agreements concluded between the various groups, territorial and professional, freely constituted for the sake of production and consumption, as also for the satisfaction of the infinite variety of needs and aspirations of a civilized being. 
Popular anarchist theorists