His influence is hard to overstate. As Sleepover mentions, he's frequently accused (and rightfully so) for his very selective historical sources, and for not doing sufficient archival work, but in general he remains an essential touchpoint for almost every historical work on punishment and incarceration, madness and psychiatry, and so forth. There are large caveats to these citations, which are often empirical objections, such as those pointed out by Spierenburg (Spectacle of Suffering, 1984). Elsewhere, it's true that many historians often cite Foucault's various writings without much further commentary, as if he's simply a necessary inclusion (and I'm certainly not alone in making this somewhat sad observation).

I'd say nonetheless that his general discursive theories - especially the power/knowledge matrix, but also practices of archaeology and genealogy - are more widely used by historians across the board, though this is merely out of the wider applicability of these notions than his more specific historical claims. That said, those aforementioned historical fields still see much worth in at least the basis of his theories, if not always in their evidence or particularities.

This question came up in my Foucault seminar early this week. While I'm sure a qualified historian can give a more comprehensive and complete answer, my professor told me that Foucault's works themselves are often considered historically problematic, as they cherry pick historical examples, but that the method is something that historians like to use.

An example of this is Irina Metzler's Disability in Medieval Europe, who in the introduction praises Foucault's methodology but criticizes him for some of the philosophical and historical content of his work.

Supplemental question:

I primarily know about Foucoult due to his connection with Nietzsche, in particular getting his genealogical method from Nietzsche. Is this his impact on history and if so how many historians look to Nietzsche?

I can at least give you my impressions from reading Foucault as a history graduate student.

Broadly speaking, Foucault has become a very malleable lens through which to view disperate academic disciplines. He seems almost analogous to Schrödinger's cat in that his writings hold the potential to mean many things, and ultimately end up realized (constrained) by the observer. Sociologists, anthropologists, literary theorists, psychologists, historians all approach Foucault with their own agendas and ultimately make of him what their agendas value.

For historians, Foucault seems to have been extremely successful in making manifest the role of forces/influences (discourses) on human events. Foucault removed specific agency through a persistent use of the passive voice and seems to have opened the door for concrete events to be sufficiently described in terms of abstracted determinants.

EDIT: Should also say the the precedent for abstracted, historic forces had already been established in academia by analytic Marxists. However, this framework was always controversial and Foucault's perspective addressed much of what was unpalatable about interpretations of history rooted in Marxism.

These are all great answers, so the only thing that I would add about the historiographic value of Foucault was his critical edge. As others have pointed out, Foucault's methodology left many historians wanting but his conclusions forced a reconsideration of methodology (say New Social History) and on topics. Even the Marxist historians of the 1960s worked within the same framework of political assumptions that had driven the narrative histories of the late 19th and early 20th century. Foucault challenge that notion with his emphasis on discourse and the location of power not merely within institutions but as u/CrossyNZ puts it as more elemental force that affects all. For example, his "What is Enlightenment" joined other works that were critical of modernity (say, the works of the Frankfurt School or Max Weber) but placed the critique on historical discourse, forcing historians to take seriously their assumptions about the intrinsic positivism of historical narratives (as stories of progress or freedom). So I would think that this critical edge is where many historians cite the influence of Foucault without necessarily embracing his methods. George Iggers' work on historiography is insightful about this in greater detail but I wanted to add in this point. Great question, by the way.

Edit: clarity

He provides a framework for interpreting the history of nation-states based around his idea of bio-power. It's a useful way to categorize some of the activities states engage in that are meant to control the population and various aspect of its population's life. These activities range from the ability of the government to imprison the population to regulation of foods and drugs like the US FDA.

Source: Class with Professor Lori Watt at Washington University in St. Louis

Based on your discussion with /u/CrossyNZ I assume you would be interested in criticisms of Biopower. It's my understanding that it is criticized for being too vague of a theory to be useful to historians. It is a description of many tools of the modern state, but does not really help to explain or analyze specific historical events.

This contains a detailed criticism of biopower including the points I made. You should probably read it for a better researched explanation biopower and its criticisms.

Aside from the theoretical impact of Foucault, which I feel other posters have discussed quite well, I think Foucault has an additional impact on history because he's quite teachable. I'm not sure if this is due to some unique property in his writing, but at both the universities I've studied at he's used as a good entry point to the incredibly nebulous field of 'post-modernism.'

In part, it helps that he wrote so widely on such a range of topics, and thus can be used in a pretty wide variety of ways. As an undergraduate and postgraduate, he was widely referenced in seminars on historiography as a thinker who's ideas challenged the conventional organisation of history whether through categorisation (The Order of Things) or bio-politics (Discipline and Punish).

In some regards, he strikes me as filling the role vacated by AJP Taylor - admired by historians for an intellectually lively approach leading to the production of pithy and disruptive conclusions. Regardless of the quality of their work, both are good at stimulating discussions and providing clear standpoints which allow you to analyse their debates with other historians.

Having gone from Foucault to dabbling (we're talking reading one or two books each here, nothing fancy) in some of his contemporaries (Lacan, Derrida, Deleuze and Guattari, Barthes), I feel that he's probably a bit more accessible, although that may well be a result of his being taught. Ultimately, Foucault is an intellectual giant and his ideas have provided a great linguistic toolkit to discuss new ways of doing history. More than that, though, he's also an excellent teaching tool because of his clearly-stated positions on issues which force undergraduates to critically assess the conventional (by which I mean the secondary-school textbook version) history.

Sorry, but have to chime in and say:

Boy, I wish I was back in serious academia and could read more about Foucault! Everyone here has such great answers.

You could divide this question into two parts. One aspect has to do with Foucault's reception by historians. I don't think that's too interesting, personally.

The other aspect relates to Foucault's vision of history which I think is very interesting. Foucault is a historian of power, or systems of power, and his interest lies in understanding all the different subtle ways they operate, especially in apparently 'unpolitical' institutions. His method consists of constructing and comparing 'diagrams' of power in order to present a picture of the most important forces operating at any given time, how they are being channelled, and how this is being described and understood.

I think where it all goes wrong for Foucault, like with any author, is when people start getting too attached to Foucault and start recycling it like zombies... But Foucault would be able to provide a theory of this process himself, observing how the collapse of the "disciplinary" societies has led to concomitant collapse in the academic disciplines...

Baudrillard's critique of Foucault is quite interesting.