Michel Foucault is usually not considered a Marxist thinker, but his thought shares some of the interests as well as ground assumption of the tradition related to Karl Marx. Foucault takes from Marxism the understanding that ideas cannot be detached from social structures and power relations (see for example his thought on power and knowledge). Unlike classic Marxist thinkers Foucault does not share the notion that the cultural super-structure is derived only from the economical base and presupposed a much more intricate relationship between culture, economy and politics. Marx thought that the economical aspect of humanity and what he called "dialectical materialism" can account for any other human phenomena. For Foucault things are not so simple and the reciprocal interaction of material and non-material aspects should be the focus of interest.
Another thing Foucault has in common with Marxist thinkers and especially Neo-Marxists (Like Adorno and Horkheimer, Walter Benjamin, Louis Althusser and others) is his interest in modern mechanisms of subordination and systems of control that do not require overt violence. Foucault asks how in a modern liberal society people still function in compliance with interests other than their own. His answer is that there are highly complex structure as play who determine how people exercise their "free" will.
Like Althusser, for example, Foucault emphasizes the materiality of power. For him power operates on the material level of existence, on the body itself (see for example his thoughts on Panopticism in " Discipline and Punish"), but this power functions through discourse. It can be argued that Foucault's discourse approach bridges the classic Marxist thought on ideology as related to ideas and the Neo-Marxist thought of Althusser who sees ideology as purely material practices. On the one hand Foucault's concept of discourse addresses ideas which shape the way people understand reality. On the other hand Foucault's discourse includes material practices and institutions.
In conclusion, although Foucault will be right to reject the title "Marxist", he can still have a place of honor in the history of Marxist thought.