The basic result is that popularity and longevity don't necessarily go together: don't forget that Dickens was outsold by several authors of whom nobody out there has every heard, such as Mrs. Craik. Others, such as her fellow Stoke native Arnold Bennett, have lingered on in academia while fading in the public consciousness. Bennett's an interesting author: a pro to-Modernist who had the misfortune to be named in a review by Virginia Woolf as a symbol of the old guard.
Mr. Bennett “has to admit that he has been concerning himself unduly with inessentials, that he has been worrying himself to achieve infantile realismbecause he cannot adapt to impressionism and modernism, which she later says appeared 'on or about December 1910' after Roger Fry's Post-Impressionist exhibition. You can read the whole wonderful essay, Mr Bennett and Mrs Brown here.
Woolf won this one: here's an Ngram of references to both authors (Woolf in red, Bennett in blue) throughout the twentieth-century:
Predicting future popularity is a mug's game, though I suspect children's books have a longer shelf-life than the average mass market adult novel - because parents and grandparents buy children the books they themselves loved, and because children feel nostalgic for books read to them. I know there are novels I hope live on, and plenty I hope don't - such as Jonathan Franzen's pseudo-literature. I have high hopes for Iain Sinclair, who I think will be seen as this century's Proust or Joyce: pulling traditional forms apart to create something suited for a confused and confusing age. In drama, again it's hard to tell - we tend to forget that Shakespeare was surrounded by equally if not more popular colleagues. Eugene O'Neill, Mark Ravenhill and Caryl Churchill will surely carry on, as will Beckett (now long dead of course) and Pinter. Further than that, who can tell?
Commodity fiction tends not to survive: Louise Bagshawe (now Mensch's) rubbish will be wholly forgotten in twenty years, though the very best in the genre may linger on. Likewise crime and related fiction: because they reflect contemporary society so well, a select few will become the object of nostalgia, as Christie, Sayers and a few others do for the pre-war era, while the rest will be forgotten. I don't think misery memoirs will be much-read either, unless on university courses (which are what confer longevity on most texts).
What's interesting is the career of the big beasts: those (mostly men) lauded as the high points of contemporary literature. I think Pynchon will survive, and probably Roth and Updike. Angela Carter and Atwood too. Some Delillo and Auster, early McEwan. I'm hoping Amis will be quickly forgotten, and Thorpe will prosper. Hensher I can't tell. Poetry? Even harder to tell, as it's so far removed from the reading public. I bet Geoffrey Hill doesn't survive, but R S Thomas and a lot of the Irish poets will. Carol Ann Duffy might make it, but surely nobody's going to read Andrew Motion in ten years' time, let alone a hundred.
The problem is that what seems important to critics and reviewers right now is unlikely to be what seems significant to future generations. What we think of as the Victorian or Medieval period would be outlandish to people from those eras. The broad outlines of a culture can't be glimpsed from the inside (and probably not from the outside): the Victorians' vision of the Medieval is very different from our version, and the next age's version will be different yet. Criteria for judgement change too, which is why only fools and bloggers make predictions.
Sadly, I think a lot of the SF I read is unlikely to be reprinted, though of course the permanent availability of all texts electronically means that some texts which however good might have faded into obscurity will survive - especially small print-run texts from marginal publishers. If they're clever.
OK, comments are open: tell me who you think will and won't make it, and who deserves to (not the same thing at all).