What a huge topic! I am only going to be nibbling on a tiny corner of it, namely authors who were deeply concerned with and influenced by philosophers. I should also say that I will immediately discount all the Boomer and Gen X authors influenced by Ayn Rand and her Objectivism (if you really want to grant her self-centered and selfish libertarianism the status of a school of thought). It could be argued that a slightly more interesting batch of novelists were the descendants of Nietzsche or rather are influenced by any number of bad interpretations of Nietzsche (I'm looking at you, Jay McInerney).
I suppose there are good and bad aspects of being overly influenced by philosophy. An author may want to tap into something larger than just the doings of certain characters that "strut and fret" across the stage. However, being bound too deeply to ideas that are of one's time can date a work so quickly, particularly if one gets roped in with a philosophy that ends up on the outs. It's kind of interesting how Thoreau and Emerson and Whitman and perhaps to a lesser extent Emily Dickinson and Nathaniel Hawthorne are all tied together with Transcendentalism. It's hard to imagine a philosophy that has less sway in contemporary America than Transcendentalism. Indeed, few people would read these authors to understand what is going on today, though many people do read them (often in a cluster) to understand what was going on in New England in America's youth. Melville is clearly another writer who went deep, drawing on a number of philosophers. I am convinced that Melville's Pierre is a direct response to Kierkegaard, but I have never had the time to write down all my thoughts on the subject. Maybe some day it will at least be the basis of a blog post.
I've hung onto a number of books of philosophy from university, though I don't have an actual plan on how to get through them. This is clearly a weakness of the TBR pile, and maybe I will open it up to more non-fiction and philosophy in, say, 2015. I'm heading into that time of life when it is time to reflect more on the meaning of life (what little there is or may be). I'm probably more likely to read those early philosophers who tended to be better writers (Plato, Bacon, Montaigne, Rousseau) than the group that followed from Hegel and tended to be crap writers (Kant and Heidegger and Wittgenstein).
For me, two of the more interesting/deep novelists of the late 20th Century are Thomas Pynchon and Don DeLillo. Both sort of tackle the issue of meaning in an era late capitalism, though they don't frame it quite that explicitly. I'm not sure either really namechecks specific philosophers (I certainly can't recall off-hand), but their books often strike me as not dissimilar from Montaigne or Rousseau where deeper meaning is extracted from everyday life. And of course, death. DeLillo's White Noise is actually quite profound in showing how people can go a little crazy when they think too much about death, particularly their own. I do plan on rereading this novel by the end of the year in a critical edition that does frame it against these big questions.
Anyway, let me turn to the original impetus for this post. I just learned that NYRB is publishing an updated translation of Montaigne's Essays, with the John Florio translation at its base. This (the Florio translation) would have been the version that Shakespeare read (assuming that he wasn't actually a super-literate nobleman who read it in French). As I discussed a bit when talking about going back to find which version of the Bible that Shakespeare used, it can be really interesting to see what the Great Authors of the past had access to, especially in cases where the translations were a bit flawed. As it happens, I have a fairly complete version of Montaigne's Essays (of which I've only read a few). This version seems a bit more complete (about 75 pages longer) and has a bit of a hook in that Stephen Greenblatt goes into some detail on how and where Shakespeare borrowed from and/or argued against Montaigne. It definitely sounds like something up my alley. So that's really all I have for today, and I apologize for not going a bit deeper. Maybe another time...