I wonder if there has ever been a comprehensive study of which authors get cited or quoted in other authors work. This does exist for academic works (most of the articles I contributed to have been cited fewer than 20 times, but four have been cited 80+ times and then two of those have hit the 100+ mark). I'm not aware of anything nearly as systematic for fictional works, not least because you don't list one's references at the back of a novel (and only in the copyright page if you quote extensively from other works). I suspect if Google really wanted to find this out, they probably could do a study, given that they have scanned most books that are still in print, but I don't think they consider it worth their time, at least not now, since it is hard to image a revenue stream that would emerge.
Now when I mean quoted or cited, I mean it in a fairly general sense, so it might mean an epigraph or sentence being quoted in another work, but it might just be a riff, like saying someone is stingy like Scrooge or even a situation is Kafkaesque.
From my recent scan of literature, I would say that a fair number of British authors, particularly from the Victorian era through 1950 or so, tend to cite Roman authors, like Horace, Virgil, Ovid or Juvenal. I'd say that has died down a bit lately, however. American writers always were a bit more likely to reference the Greeks (particularly Homer) but that also seems to have declined a bit and Greek and Roman literature (and even Chaucer and Dante) is not really part of the curriculum any longer.
I suspect Shakespeare remains in the top position, even among American writers.
Lewis Carroll is probably not that far behind, since so many authors want to explore dreamlike states, and Alice is a convenient shorthand reference.
I'm not sure what the list looks like after that, but I'll offer up some thoughts.
I suspect Kafka is the single most influential and/or cited "foreign" author among writers working in English. I could certainly be wrong, of course.
I suspect that Dostoevsky far outpaces Tolstoy, Turgenev and Chekhov as far as Russian influence in English literature. In terms of specific Dostoevsky works, it is probably Crime and Punishment in the lead, then the Brothers Karamazov with The Double and Notes from Underground fairly far behind. I don't think Demons is particularly influential anymore, which is a shame, as it is a bit of neglected masterpiece.
Bulgakov's The Master and Margarita seems to be gaining in influence, which is well deserved.
It's kind of interesting that when Hemingway is invoked, it is sort of for the whole of his oeuvre as well as his macho image, whereas when Fitzgerald is referenced it is virtually always in regards to The Great Gatsby.
While Dickens has certainly generated quite a lot of interest in a wide range of his characters, the ones from A Christmas Carol do sort of eclipse all the rest. The same could be said for Mark Twain and Tom Sawyer and Huck Finn.
At least people do read their other works, for Mary Shelley and Charlotte and Emily Bronte, they are all defined by just one novel each, which is a bit unfortunate no matter how great those novels are. (I suppose it is still better to be a one-hit wonder than to not have that level of success in the first place...) Orwell is more of a two-hit wonder with 1984 and Animal Farm being quite influential, but with his other novels and essays being generally neglected.
I would say Faulkner may be at a low point now, as I certainly haven't seen too many other novels reference his characters (though perhaps I do remember coming across a reference to epic stubbornness that was actually a reference to As I Lie Dying). (Other long and fairly complicated novels such as Moby Dick* and Ulysses have somewhat fallen out of fashion these days.)
I really don't think I could hazard a guess at which poets are still cited, though I do see T.S. Eliot (especially The Waste Land) pop up from time to time, as well as Walt Whitman.
Anyway, this is what I have come across in my relatively recent reading. I am happy to make corrections based on submitted comments.
* Melville's character Bartleby the Scrivener does have legs, however.