This has always been a difficult question for me. I'm not a literature student, so I don't choose novels based on my professional life. Plus I'm not a good critic, at least the kind who discerns symbolism or archetypical themes or a plague of fantasies. I suppose I notice familiar philosophical themes when they appear, but I basically just take the naive approach of following the narrative. This tends to give me a (blind?) freedom to enjoy a wide range of literature.
My exposure to English courses was very limited in college. As an undergrad I took basic composition and an English language poetry survey. As a doctoral student I took a course on Kenneth Burke from David Blakesley and a team-taught literature and philosophy course with Paula Geyh (a great experiment in juxtaposition: Homer and Adorno, Dickens and Marx, Cixous and Wittig, DeLillo and Baudrillard, Derrida and Foucault and Calvino). But, that was it. I actually felt a panic of my literary ineptitude after graduating with my BA, and I started reading everything I thought might be important. I read everything Faulkner wrote that was set in Yoknapatawpha county. I read the Russian Masters and a bunch of Nabokov and Mishima and Joyce and Kafka and Garcia-Marquez. For lighter fare, I started reading Tom Robbins and John Kennedy Toole and Naipaul. I realized I hadn't read any women authors, and felt ashamed. After a short while gorging on all-male literature, I got hooked on the philosophy of Gilles Deleuze, then Foucault, and then into the whole postmodernism scene as endlessly debated in the early 1990s. Then I studied philosophy of art for my MA before going on to work with Deleuze, rhetoric, space, and phenomenology during my doctorate.
All of this biographical rambling brings me to two points based in the comments in that book meme that has been going around, and both are related to the question posed in the title of this post. The first has to do with a large set of classics of literature that I said I probably won't read. I don;t suspect I'll read these books, not because I have something against their greatness, but because I feel like I missed my opportunity to experience them as a younger person. I just feel like a lot of books have a best chance of being read as a high school student or while in college. I didn't read much fiction at that time (humanities courses were my academic weakness in high school). And now I tend to read things that are very recent, so I don't know if I will ever get on a classics kick again.
The other issue has to do with an interest in both literature and philosophy from the first part of the 20th Century (before WWII). For some reason it seems that a lot of interesting things tend to happen before periods of gigantic crisis that relegate literature and philosophy to obscurity. A lot of work by philosophers like Husserl, Scheler, Whitehead, Bergson, and Benjamin prefigure a lot of the ways of approaching phenomena that we see in contemporary cultural studies and humanities work. And I suspect that the same can be said for literary authors of that time, who were living responding not only to the crises of economic depression between two world wars, but also the rapid changes of industrialization, new modes of representation and communication, urbanization, immigration, propaganda, and commercialization. So, I have books on my shelf by people like Bulgakov, Nathanael West, Nella Larsen, and Kafka. I think that the two sets of books will probably have a lot to say to each other, not to mention the way they will surely be seen to have been influential in one way or another on the 60s and 70s authors that have so influenced my own thinking and research.