The Collaborative International Dictionary of English v.0.48:

Anarchist \An"arch*ist\, n. [Cf. F. anarchiste.]
   An anarch; one who advocates anarchy of aims at the overthrow
   of civil government.
   [1913 Webster]

WordNet (r) 3.0 (2006):

anarchist
    n 1: an advocate of anarchism [syn: anarchist, nihilist,
         syndicalist]

Moby Thesaurus II by Grady Ward, 1.0:

67 Moby Thesaurus words for "anarchist":
   Bolshevik, Bolshevist, Bolshie, Carbonarist, Carbonaro, Castroist,
   Castroite, Charley, Communist, Cong, Fenian, Guevarist, Jacobin,
   Leninist, Maoist, Marxist, Mau-Mau, Puritan, Red, Red Republican,
   Roundhead, Sinn Feiner, Trotskyist, Trotskyite, VC, Vietcong,
   Wobbly, Yankee, Yankee Doodle, anarch, anarcho-syndicalist,
   antinomian, bonnet rouge, criminal syndicalist,
   extreme left-winger, extremist, frondeur, insurgent,
   insurrectionist, left-wing extremist, lunatic fringe, malcontent,
   mild radical, mutineer, nihilist, parlor Bolshevik, parlor pink,
   pink, pinko, radical, rebel, red, revel, revolter, revolutionary,
   revolutionary junta, revolutioner, revolutionist, revolutionizer,
   sans-culotte, sans-culottist, subversive, syndicalist, terrorist,
   ultra, ultraist, yippie