Matthew Cheney has an interesting post on the conventions of infodumping (which, as he later notes in the comments, needs to be distinguished from simple "exposition"). Infodumps are a vice especially characteristic of a certain type of nineteenth-century British historical novel, what Rosemary Mitchell calls "conservationist": take one guidebook or historical text, drop it into the middle of the narrative (while, as you might expect, the plot grinds to a screeching halt), then continue on. Mitchell is referring specifically to W. H. Ainsworth, but other novelists, like Edward Bulwer-Lytton (see The Last Days of Pompeii, for example) and G. P. R. James, are equally guilty as charged. Such large-scale antiquarian infodumping finds its complement in other forms of historical digressiveness, all presumably intended to produce what Barthes called the "reality effect"; my pal Emily Sarah Holt, for example, suddenly swerves into minute descriptions of costumes and recipes, and certainly one of the frequent charges against George Eliot's Romola has been that the 3x5 cards are a little too evident. Yet another variant is the theological and/or polemical infodump, as practiced by William Sewell in Hawkstone (character one asks a three-line question, character two goes on for pages about ecclesiastical history...) or Catherine Sinclair in Beatrice (you wouldn't believe what those Italian Catholics get up to!).
What separates such infodumping from "exposition," I think, is that the info in question rarely has anything to do with plot, characterization, and so forth; instead, infodumps tend to indicate moments when the fiction simply fails as a vehicle for the author's manifest intentions. "[F]lat-out bad writing," yes, as Matthew says, but also a total collapse of the fiction qua fiction. In historical fiction, for example, writers frequently succumb to infodumping as a means of importing "objectivity" into the novel--look, ma, facts!--even though historical fiction is frequently at its most interesting when it is most subjective and reflective. Infodumping often reduces history to a list of facts, whether facts about wars, people, or murals; the work of narrative and interpretation temporarily goes by the wayside (and, in some historical novels, the infodumped material doesn't assist the reader with interpretation at all). In novels with didactic aspirations, moral infodumping allows the author to shut down alternative interpretations of the text--or, at least, allows the author to try. (Needless to say, it doesn't always work.)
On a different tack, one of my favorite bits of exposition in a historical film comes from The Madness of King George. Margaret Nicholson has just tried to assassinate the king:
PITT: Your Majesty.
KING: Ah ha, Mr Pitt. Well you've had a lucky escape, what, what?
PITT: I, Your Majesty?
KING: Yes, you. You're my Prime Minister. I chose you. If anything happens to me, you'll be out, what, what, and Mr Fox will be in, hey, hey .
This little exchange is terrific because it's so economical. Bennett hits on exactly the one thing modern audiences aren't likely to "get," dispatches it in a few lines, and does so amusingly, to boot. Moreover, the dialogue fits smoothly into the film's structure: it suggests that Pitt's cool "The King will do as he's told, Mr Fox" (9) isn't entirely the right reading of the situation, and inaugurates the king's film-long habit of poking sly fun at his deep-frozen PM.
 Alan Bennett, The Madness of King George (London: Faber and Faber, 1994), 11.