Bertolt Brecht is typically discussed as a Marxist. It ain't quite right, and I'm going to tell you why.
Allow me to be more specific: It's sort of right, but it's a misleadingly incomplete assessment. Was Brecht a Marxist? Did he study Marxism, did he live in the DDR, did the world view he put forth in his works sometimes reflect elements of Marxism? Yes, yes, I know. More or less true on all counts. But it is unfair and inaccurate to discuss Brecht strictly as a Marxist, especially when he was such a half-assed one. Rather than translate my recent (and annoying) 9-page research paper on the topic from German (your eyes must be tired from the very nice writeups above), allow me to condense it for you.
I would be quicker to call Bertolt Brecht an anarchist - it's painfully obvious in his earlier works. Even his later works kept up the trend, though most readers jump to the conclusion that they exhibit more of a Marxist slant. Do Brecht plays and poems consistently bash capitalism? Yes. Do they glorify the working class? No. Do they hint that communism is the solution? No. Brecht consistently shows his distrust of authority, Marxist or otherwise, and his disapproval of any war of conquering.
When he decided to study Marxism in the 20s, he did so under a fellow by the name of Karl Korsch, a dissident exile from the Communist Party. Why? He wanted a perspective that would not be tainted by a bias toward a certain body or particular party. Brecht sincerely admired Karl Marx, but this does not mean that Marxism is the only way to analyze what Brecht wrote. According to his journal and friends of his, he only saw communism as the "best available solution" for the rise of militant fascism in his time.
I'll say it again: Brecht was a half-assed Marxist by most standards. While living in East Germany, where the government tried to paint him a Marxist hero of literature, he maintained a Swiss bank account and forwent no luxuries. He shamelessly (and truthfully) denied any allegiances to any communist party when called before the House Un-American Activities Committee before leaving America, and weaseled out of being charged with anything by playing up his bad English, dancing around questions, and generally offending the court (with a lit cigar and dirty overalls, among other things). He wrote poetry that "subtly" criticized his own East German government. He wrote fervently against nuclear weapons of any size and shape, directly criticizing what a hard-line Soviet might call a symbol of Soviet might. These are just events from his life - for some real good stuff, read some of his plays, and try not to think of him as a Marxist. You might be surprised.
Sources:
Brecht HUAC Hearing (Audio Recording). Retrieved March 20, 2008, from http://commons.wikimedia.org/wiki/Image:Brecht_HUAC_hearing_(1947-10-30).ogg. USA: House of Representatives, House Un-American Activities Committee.
Brecht, B. (1988). Sammlungen 1938 – 1956 (Vol. 12). (J. Knopf, Ed.). Frankfurt am Main: Suhrkampf.
Gerz, R. (1983). Bertolt Brecht und der Faschismus. Bonn: Bouvier.
Hecht, W., Bunge, H., & Rülicke-Weiler, K. (1969). Bertolt Brecht: Sein Leben und Werk. Berlin: Volkseigener.
Kebir, S. (2004). Und Nun ist Krieg. In J. Niehaus (Ed.), Brecht und der Krieg: Widersprüche damals, Einsprüche heute (pp. 8-15). Berlin: Theater der Zeit.
Knopf, J. (2006). Bertolt Brecht. Frankfurt am Main: Suhrkampf.
Münkler, H. (2004). Der Dreißigjähriger Krieg, die neuen Kriege, und Brechts MUTTER COURAGE. In J. Niehaus (Ed.), Brecht und der Krieg: Widersprüche damals, Einsprüche heute (pp. 8-15). Berlin: Theater der Zeit.
Schumacher, E. (2006). Mein Brecht: Erinnerungen, 1943 bis 1956. Berlin: Henschel Verlag.