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I'm a bit taken by Nietzsche's philosophical skepticism, which is skeptical even of scientific knowledge. I've come to believe that the more rigorous you are in your thinking, the more skeptical you must become.
But has philosophical skepticism died out or are there notable proponents since Nietzsche?
After a quick search for skepticism it seems that the term is heavily peroidized, referring to the school of Pyrrhonism in the 1st BC its subsequent rediscovery in the 17th century. So it seems there aren't really any contemporary philosophical skeptics (although in some abstracts of papers on skepticism I found Marx and Derrida came up). Its possible the term has degraded since skepticism is usually supplemented with some sort of empiricism or realism and where it isn't it typically manifests as nihilism.
I've become rather hesitant to define François Laruelle's non-philosophy since I don't want to misrepresent it but I will offer it here as the most contemporary thinking through of the implications of what you called Nietzsche's philosophical skepticism (although I would define Nietzsche's project more as an anti-philosophy).
One of the basic gestures of non-philosophy is to critique the notion of thought's "sufficiency" to comprehend and conceptualize reality (the "Real"). Put in overly simplistic terms, it posits that the Real is foreclosed to thought and is thus unphilosophizable. The only way it becomes philosophizable or conceptualizable is if it is "decided" which is the inaugurating gesture of all systematic philosophies. I won't go on from there but you can see how it takes up the themes of certain skeptical philosophies.
The most representative work is Philosophie Non-Standard which sadly remains untranslated but The Principles of Non-Philosophy was recently translated into English and is considered the most advanced presentation of Laruelle's thought.
Deleuze and Guattari are also a good place to look for philosophers taking up the style and thematics of Nietzsche (although this can be said of most of the French theory that emerged in the late 60's) but are hardly as readable. If you are feeling more poetic, I would look into E.M. Cioran. In terms of a contemporary "rigorous" empirical skepticism, there is no one better than Wittgenstein. If you want to go back to the historical manifestations of skepticism with some contemporary commentary, Richard H. Popkin looks like a good place to start (though I haven't read him myself).
Peter Unger is one of the more serious proponents of contemporary scepticism about knowledge , i.e. the thesis that (necessarily) nobody ever knows that anything is so.
His main argument for scepticism runs as follows (each claim is to read as preceded by the necessity operator): If someone, x, knows that p, then it is alright for x to be certain that p. It is never alright for x to be certain that p. So, x never knows that p.
For Unger's defense of this argument and more on his position see Unger's monograph Ignorance.
Since another (Peter) Unger was mentioned before and I want to counter the impression that critical theory is the only game in town, here is a quote from Roberto Mangabeira Unger (from The Self Awakened) where he expresses skepticism opposite the idea that we can arrive at correct understanding of what goes on at far reaches in space or far distances in time:
This [scientific] investigation carries us to orders and magnitudes of reality far removed from the setting of human life in which imagination can remain wedded to action. Now inquiry leaves action far behind, and with this overreaching begins to draw pictures of the world that no longer remain in communion with our experience of manifest reality. Or it remains in such communion only be conjecturing a long series of links between those pictures and this experience, explaining, at the end of the chain of conjecture and experiment, how we can perceive the world one way when it is in fact another way.
As far as I can tell he is skeptical of naturalism, i.e. also "skeptical even of scientific knowledge" (e.g. the idea that laws of physics never change). I don't think there is a direct link to Nietzsche's philosophy (or his style of philosophy) though.
UPDATE This recent article (in German, Google translation here) remarks on Nietzsche's influence on famous mountaineer Reinhold Messner, whose 70th birthday is today. Messner's many books also touch on questions of philosophy, e.g. the individual’s power against conformity (less so on skepticism).
On reflection, I now also think that there may be a relevant link between Roberto Mangabeira Unger and Friedrich Nietzsche, e.g. apparent in the first author's call to "life in such a way that we die only once" (but attenuated by his emphasis on community): Reinhold Messner would certainly agree to that call and he lived a life to show it: Happy birthday!
