Honestly, I get annoyed at the idea that types of writing ever end. (Mornngstar already mentioned this, but long ago). They don't. We still have romances and realism (most of "literary" fiction is a largely unexamined realism, though some is slightly self-conscious, but still just straight up realism). There are still works that are straight up naturalism, and continuations of Modernism. Etc. I do not think it will come to an end, though like many particular branches of literature, it has waned in prominence, and will probably never regain a position as it had before.
A lot of the consideration of the postmodern here has focused on really shallow things, or missed the point entirely. While metafiction and the questioning of reality are components, they aren't really the drivers of postmodernism. Only a few particular, weird, stalwarts are ready to go and dub things like Don Quixote, Tristram Shandy, Joseph Andrews, etc. as being "postmodern." Primarily, no one seems to have talked about what is perhaps one of the most absolutely important parts of post-modernism, which is its focus on history. In one of Frederic Jameson's most famous chapters (in his tedious though brilliant, very long book: Postmodernism), he examines post-modern literature through post-modern architecture (Linda Hutcheon also carries this argument on, it should be noted), and points out that while in Modernism, the sense of progress means a breaking away from old ideas and creating "new" ideas, things never seen before, etc., in Post-modernism, they examine the "old" idea in a new way: Ie: a Neogothic catheral, but made of steel and sheet glass instead of stonework. It is this integration of history with an examination of it (not a carrying it forward, as you might see with something like neoclassicism, for instance) as both present and past, relevant and not, that really defines postmodernism. This is why the focus on historical revisionism, fairy tales, and the like has played such a huge part. This builds to what I think is absolutely key, and can be found in John Barth's incredible essay "The Literature of Replenishment" in which postmodernism is a "synthesis or transcension of [the] transcension [that is found within modernism (or other movements, largely)]" and is a "self-transcendent parody," which I think gets simplified into irony, but isn't: rather, it is something that begins in parody (pastiche/satire/etc.), but ends up transcending these boundaries to hold the past and the present as bound together.
Which is all too long of a paragraph to write about that. But I have particular ideas, and find that most people that say things about postmodernism have read only a handful of the postmodernists, and have generally read very little of the theory surrounding it. And it's a topic close to my heart and research interests, so...
Now, as to where does literature go from there: Look at what it's been doing. Postmodernism was most alive and kicking in the 60s through early 80s, and has been dying off since. The main people to go to have been Pynchon, Coover, Barth, Carter, Calvino, Gass, , etc., and while there have been those who have written later who fit the bill (Delillo, early Ondaatje, Wallace, etc.), the movement has been largely muted. In that space we're seen Magical Realism, New Sincerity, L=A=N=G=U=A=G=E (associated with poetry, but connected to and filled with lots of prose), postcolonialism, etc. Some has stuck and some hasn't. Sometimes these are deliberative affectations (I'm thinking particularly of Tom McCarthy's International Necronautical Society and their silly little manifesto), but generally there are trends. Who the hell knows where it will go, but contemporarily, people are very concerned with trust and marginal beliefs, where we narrow our view of belief to such a degree that we become largely blind (I guess you can see how I feel about this), but who knows? Movements are identified after they are done, for the most part. I like that. Who wants the responsibility of crafting the future of literature AS WELL AS a thoughtful and interesting novel?
