As a philosopher, Nietzsche was one of the great critics of metaphysics, something that was picked up on by a number of leading twentieth century philosophers of otherwise diverse views for example, Wittgenstein, Heidegger, and Carnap. Having said that, he wasn't entirely successful in freeing himself of metaphysics. His famous notion of the "will to power" as used by him in his various writings looks pretty metaphysical. On the other hand he made a great contribution to social science with his studies of the geneology of morals, something which was considered to be very daring and shocking at the time. BTW his analysis of the geneology of morals fits in rather well with Marxists' analyses of ideology IMO.
For a long time many analytical philosophers in the Anglophone world tended to be rather disparaging of Nietzsche as a philosopher. This was true particularly of such figures as Bertrand Russell and A.J. Ayer (who dismissed him as "wooly minded"). On the other hand Ludwig Wittgenstein was a great admirer as was the logical positivist Rudolf Carnap. Thus concerning Nietzsche, it is interesting to note that while Carnap went after Heidegger in his essay. "The Elimination of Metaphysics Through Logical Analysis of Language," he had nothing but praise for Nietzsche. There, Carnap discerned similarities between Nietzsche's critique of metaphysics as found in say *Human, All too Human* and his own. He seems to have regarded Nietzsche as a "metaphyscian" who had the good sense to avoid the errors for which he reproached other metaphysicians. He admired the "empirical content" of Nietzsche's work, including especially its "historical analyses of specific artistic phenomena, or a historical-psychological analysis of morals." And he praised Nietzsche for having chosen the medium of poetry in such works as Thus Spake Zarathustra for presenting his ideas rather attempting to present them in a theoretical treatise. The fact that Carnap found much to praise in the work of Nietzsche is significant since in "The Elimination of Metaphysics Through Logical Analysis of Language," Carnap went on the attack against Heidegger, whose metaphysical statements, Carnap dismissed as meaningless. Apparently for Carnap, part of Nietzsche's greatness was the fact that he used poetic means for expressing himself. This fit in with Carnap's view that metaphysics fails because it makes meaningless statements. For Carnap, language had a variety of functions to perform. One of those is the making cognitively meaningful statements. Other functions include the making of what Carnap described as emotive statements. Such language can express Lebensgefühl. Metaphysics attempts to express Lebensgefühl too but fails because it can only issue meaningless statements. The appropriate means for expressing Lebensgefühl is through art rather than metaphysics, and Nietzsche was praised by Carnap for realizing that. For Carnap, Nietzsche was the metaphysician who had the greatest artistic talent.
Some time ago I read Arthur Danto's Nietzsche book. There Danto makes the point that Nietzsche in his work anticipated some of the central ideas of 20th century philosophical movements such as logical positivism and existentialism. Curiously, enough, I could find no reference in Danto's book to Carnap. I wonder what was up with that. Anyway, Danto's 1965 book was, I belive, the first full-length study of Nietzsche by an analytical philosopher. Since then quite a number of analytical philosophers (such as the Nehamas book that Andie cited) have written studies of Nietzsche's work, so that it is no longer the case that the field of Nietzschean studies is a monopoly of continental philosophers as had been the case prior to Danto's book.
It is also important to point out that while Nietzsche was politically a kind of reactionary and that his writings had a great appeal to certain kinds of reactionaries including the Nazis, his work also had a great appeal to many leftwing intellectuals. As early as the 1890s, there were discussions underway within the German SPD as to how his thought could be used to promote socialism. During the twentieth century, Nietzsche was taken up by many leftists starting with such folk as Lunacharsky, Bogdanov,Trotsky, Bukharin, and a number of other Bolsheviks. He was a major influence on the young Lukacs (who later became a great critic of him). Nietzsche was greatly admired by the Frankfurt School (i.e. Adorno, Horkheimer, Marcuse), as well as by Sartre. And of course people like Foucault and his disciples styled themselves as "Nietzscheans."