People on the far left, anarchists and other left libertarians, have had a pretty critical view of Marxism, with the difference being that anarchists tend to be critical of all of Marxism while others, who incorporate Marxism into their view of the world, are critical of particular types of Marxism than Marxism in general. I'm going to deal with the Anarchist critique of Marxism.
The way that I see it Marxism is opposed not because it's a bad doctrine or something which unrealistically reflects reality but, on the contrary, because it's all too good at explaining reality. What I mean by this is that Marxism, through the extraordinarily prolific writings of Marx, from the Communist Manifesto to the enourmous effort of Capital through smaller works on politics and economy and newspaper articles, presents a ready made, sophisticated, critique of society which, while valid, confers on the person who has gone through all these writings a power differential in relation to people who haven't.
Two people come into a room for a meeting: one is a progressive or an anarchist who has just been active in fighting for social justice on the local level and has his or her own ideas about society and capitalism; the other is a person well versed in Marx, who doesn't necessarily have that much experience actually taking on injustice but instead has amazing ideas about the causes of injustice, the way the system works, etc.. What has the potential of happening in that situation is that the Marxist, although he or she may not actually have been the most effective activist, will, because of the theoretical sophistication of the worldview which he or she brings with him/her will appear to be the better activist and will therefore be more likely to take over the meeting and use the meeting for his or her own purposes.
Marxism creates a power differential between people which is based on knowledge. The progressive or anarchist who has strong feelings for social justice but can't articulate them as well as the Marxists faces the possibility of looking stupid or looking inarticulate or irrelevant in comparison to the greater knowledge brought forward by the Marxist, even if, in terms of actual work being done in the community, the progressive or anarchist may be much more productive and much more effective in doing positive things for social change in their community.
It's not that Marxism is some sort of irrelevant doctrine but that because it has a theoretically sophisticate cannon, which is physically huge, what's right about it can be articulated easier than political traditions who don't have something like Capital at their disposal can. People who don't have Capital at their disposal will probably have a hard time of really answering the ideas of the Marxists in a convincing way. But that should not be the point. The point should not be who can give the best way of relating to society at large, the system which we live in, but who can work to change it most efficiently.
This goes double for Marxist-Leninists. Leninists will often make point that Leninism is a sort of guide for action while Marx deals more with theoretical issues. Leninism in this sense provides a ready made guide for action and strategy. Someone who has absorbed the most coherent parts of Leninism will be able to reel off strategies and ideas about tactics and action which mere mortals who just live in the real world aren't able to do. But in Leninism, because it deals with action in a pre-conceived way, the objection to it isn't only that it creates a power differential but that its power differential has the capability of sabotaging potential actions and campaigns for social justice by putting a decades old strategy from a country which has almost nothing to do with the U.S. in terms of political history in place instead of really reflecting on current situations and current issues within the U.S. and evolving something which actually fits with U.S. reality. To say it simply, the power differential in Leninism isn't just obstructionist, it's potentially the kiss of death because it substitutes old, albeit in their own way sophisticated, ideas of strategy which have nothing to do with the United States for actual, relevant, thought on how to change society right here, right now.
The organizer who studies things and tries to come up with what he or she thinks is a potentially effective way of organizing people for social change knows what the issues are; coming into a situation like the hypothetical one with the Marxists and the anarchists and progressives this organizer potentially faces the situation of being outmaneouvered by Leninists who, while they may have read Lenin, may have had no experience whatsoever in organizing but who who can present a sophisticated sounding analysis of what to do and why.
And that's the trouble with Marxism and Marx-Leninism: they create situations of privilege and power which marginalize sincere people who are working for social change.