David Hume is said to have set the foundation for much of what passes as Skeptical thought these days. If that means, much of what Hume says is repeated practically verbatim by today's Skeptics, that is quite correct. Arguments against the miraculous have not progressed a great deal since Hume, although skill and rewording his verbiage into different forms abounds.
Since so much has been written addressing Hume's views that we could certainly not supersede (ranging from C. S. Lewis' Miracles to the more recent In Defense of Miracles collection of essays), our comments about Hume shall be brief.
Hume was of course a child of the Enlightenment, that period when it was first thought that man might be able to perfect and improve himself and the world through applied reason and science. The corresponding theological premise was deism, as evolutionary theory had yet to provide the excuse needed to make atheism intellectually possible.As Hume puts it: "Man is a reasonable being, and, as such, receives from science his proper food and nourishment."
Not to doubt that knowledge is of its own a sort of growth mechanism, knowledge and its pursuit (may I say from experience) offers something of a semblance of fulfillment, if only because it has in view a goal (acquisition of knowledge) that will never be completed and has the semblance of the infinite.
Foundational to Hume's case is the argument that "every idea which we examine is copied from a similar impression." Thus:
The idea of God, as meaning an infinitely intelligent, wise, and good Being, arises from reflecting on the operations of our own mind and augmenting, without limit, those qualities of goodness and wisdom.
In other words, our idea of God is not the result of revelation, but of us taking the normal attributes of ourselves and increasing them to infinity.
Now one may note right away that Hume's argument implies a sort of genetic fallacy, if taken to the extreme (not clearly pursued by Hume, at least not here, but indeed elsewhere) assumes that explaining how an idea of God might have come up equates with disproving that God actually exists. Readers of Lewis' Narnia series, specifically The Silver Chair, will recall from that book a scenario in which captives in an underground world who were trying to describe the sun compared it to a globular light source that was present in the room; from this the villian in the series argued that the sun itself had not actually existed, or been seen by the heroes, but was a copy of what they saw before them, heightened by their imagination.
The implication being that there is indeed imagination at work, but it can just as easily be ascribed to the Skeptic -- they say we are inventing God; we may reply that they are inventing psychological theory.
The next major stage in Hume's overall thesis is the premise that "causes and effects are discoverable, not by reason, but by experience" -- and this leads to the main isse Christians have had with Hume, for he says he cannot believe in the resurrection of Christ, having not seen it himself: "...it is a miracle that a dead man should come to life, because that has never been observed in any age or century."
But, we may ask, what of apostolic testimony to the resurrected Jesus? Hume's answer: "...(N)o testimony is sufficient to establish a miracle unless the testimony be of such a kind that its falsehood would be more miraculous than the fact which it endeavors to establish." And here is how else Hume solves that problem:
...(T)here is not to be found, in all history, any miracle attested by a sufficient number of Men of such unquestioned good sense, education, and learning as to serve us against all delusion in themselves; of such undaunted integrity as to place themselves beyond all suspicion of any design to deceive others; of such credit and reputation in the eyes of mankind as to have a great deal to lose in case of their being detected in any falsehood, and at the same time attesting facts performed in such a public manner and in so celebrated a part of the world as to render the detection unavoidable...
Christian "resurrectional" apologetics, of course, has thoroughly answered Hume on half of these points, and the other half are clearly little more than Hume's personal prejudices. Re: "good sense, education, and learning" -- Hume has references (that sound rather bigoted today) to "barbarous and ignorant peoples"; yet how much "education" does it take to see that a dead man is alive, and at any rate, what of Matthew and Paul?
Re: "celebrated part of the world" -- Palestine was a major crossroads, but it hardly makes a difference. But all of that may have meant nothing to Hume anyway. It is quite revealing that even when he offers a hypothetical situation where these conditions are met (Hume hypothesizes a situation in which the Queen has supposedly died and come back to life), Hume admits he would be surprised, but "should not have the least inclination to believe so miraculous an event." He would "still reply that the knavery and folly of men are such common phenomena" that he would rather believe that it was a conspiracy than a miracle.
Hume laid the foundation for many moderns who take anything, no matter how offbeat (Jesus was a space alien) or uninformed (The Da Vinci Code) and find it preferable to the Christian faith. Whether that faith is right or wrong in this context is beside the point: The point is that the preference for the unreasonable, the outrageous, and the theoretical against the evidence available is nothing new. Hume was just one major name that encouraged that line of thinking in modern Western society.
I have found this evaluation of Hume confirmed by a highly techincal book by John Earman, a professor of history and philsophy in science, titled (without any hint of embarrassment) Hume's Abject Failure. Earman is no Christian, and says, "If I had need of Gods, they would be the Gods of the Greeks and the Romans." His motivation, rather, is to "set the record straight and frame the issues in a way that makes discussion of them more fruitful" -- as well as react to the "pretentious sneering" he perceived in Hume.
Earman's principle objection is much the same as my own: "An epistemology that does not allow for the possibility that evidence, whether from eyewitness testimony or from other source, can establish the credibility of a UFO landing, a walking on water, or a resurrection is inadequate."  I have said much the same to Skeptics, such as one that seemed to think apologetics for Christianity are immediately ended by asking us whether we'd believe it if 500 witnesses said they saw a mouse pick up a battleship. This critc could never answer my question, "If indeed a mouse did pick up a battleship, how could we, by your strict criteria, ever believe it?"
Contemporary critics of Hume sensed the immediate weakness in his arguments and retorted with an example of a prince from a tropical climate who had never seen ice. By Hume's reasoning, the prince is just as validated in not believing in ice as the modern Skeptic might be "validated" in rejecting miracle testimony. This retort has such strength that Earman calls it an "embarrassment" and he notes Hume's efforts at sophistry in trying to evade the force of the argument .
Hume tried to avoid the problem by noting that ice was not outside the experience of northern peoples; Earman retorts that if this is so, then if homo sapiens arose in Africa, "there was a stage in human history where the total collective experience of the species coincided in relevant respects" with that of the prince who lived in a tropical climate.
In addition, we would add that Hume as much as undermines his own argument from experience, for it is just as well to say that a resurrection was "within the experience" of the Apostles -- leaving Hume with nothing but calling people names ("barbarous").
Likewise a failure was Hume's attempt to argue that for the prince, the existence if ice might be deduced by analogy: "If one sees a positive analogy for a solid form of water in other phase changes, why not see a positive analogy for resurrection in near death experiences, catatonic states, and the like?"  It is well to highlight Earman's summary statements in closing [70-1], even as he praises Hume for at least identifying an important problem and dealing with it in an interesting manner:
In 'Of Miracles,'Hume pretends to stand on philosophical high ground, hurling down thunderbolts against miracles stories. The thunderbolts are supposed to issue from general principles about inductive inference and the credibility of eyewitness testimony. But when these principles are made explicit and examined under the lens of Bayesianism, thet are found to be either vapid, specious, or at variance with actual scientific practice...[Hume] was able to create the illusion of a powerful argument by maintaining ambiguities in his claims against miracles, by the use of forceful prose and confident pronouncements, and by liberal doses of sarcasm and irony....
I find it ironic that so many readers of Hume's essay have been subdued by its eloquence...No doubt this generous treatment stems in part from the natural assumption that someone of Hume's genius must have produced a powerful set of considerations. But I suspect that in more than a few cases it also involves the all too familiar phenomenon of endorsing an argument because the conclusion is liked. There is also the understandable, if deplorable, desire to sneer at the foibles of the less enlightened -- and how much more pleasurable the sneering if it is sanctioned by a set of philosophical principles!
I have also had access to back issues of a journal of professional historians titled History and Theory, which is of interest because it is clear that at least one professional historian does not agree with the arguments of Hume and modern materialists who insist that miracles must be ruled out a priori as possible causes.
In the October 2005 issue (373-390). Aviezer Tucker offers and article titled, "Miracles, Historical Testimonies, and Probabilities." Of interest is the point made to begin that Hume, who first wrote a history of England as a historian, in later analysis was found to be someone who seemed "sloppy and uncritical of his limited sources; he had not found all the relevant evidence and had not compared sources critically. He appeared to be an amateur."  This is relevant because as Tucker notes, Hume's treatise on miracles uses methods that have "more to do with his historiographical than his philsophical works, and consequently share some of the same problems as his historical writings," including a "pre-scientific, indeed ahistorical approach" to the topic. (Tucker also notes that certain parts of Hume's essay are "ambigious.")
Tucker then goes on to argue -- in the same vein I have in other venues -- that Hume's definition of miracles is inadequate. "Ancient Hebrews and Greeks had no concept of a universal immutable law of naturem let alone a concept of events that violate such laws."  Tucker proposes instead that miracles be defined with a "method of cases" using descriptions of miracles to decide what they are. He lists several, such as prophecy, resurrections, transmutations, and the parting of the Red Sea, and then points out that "none of these 'miracles' is in violation of the laws of nature, as Hume claimed"  -- for indeed, science has reproduced the effects of miracles, and may conceivably come up with ways to reproduce others, such as transmutations.
There is not even a law of nature that "explicity contradicts" resurrections. This, again, has been my own argument for quite some time. In contrast, Tucker notes, science fiction stories often contain the same sort of "violations" of laws of nature (such as faster than light travel) but no one things that sci-fi authors are writes of "miracle tales."
Thus it is that Hume's definition of a mircale is "clearly anachronistic, ahistorical."  Tucker opts instead for a definition that matches my own: Miracles are "divine feats of strength"  and proofs of God's power. If Hume's apologists do not use this definition, then they are talking about something that has "nothing to do with what Jews and Christians have been talking about for almost all of the past 3,000 years" and "his discussion has no relevance for the philsophy of religion, or as a critique of traditional Judeo-Christianity, or for the way historians and philsophers of history should proceed with claims that a miracle has occurred." 
All of this changes the rules, so to speak, for the prior probability of a miracle happening in the way that Humean apologists argue. Whether a miracle can be historically decided to have occurred goes back to other criteria, such as the existence of independent witnesses, number of testimonies, and so on.
Tucker, we might note, decides that critical Biblical miracles are lacking on these criteria  and is sympathetic to theories about the composite origins of the Pentateuch  and the New Testament . In the end he argues that "the best explanation for many other miracles stories may be that for political, religious, and institutional reasons they were written hundreds of years after their alleged occurrence."  He even makes the incredible claims that "stories of divine death and resurrection were ride in ancient Near East mythology" and says that the "resurrection has no Jewish precedents" (!) and "may have been introduced later to convince a pagan audience of the divnity of Jesus". This is how he thinks the miracle events may be better explained -- not by Hume's methods of dismissal.
Of course we would dispute Tucker's conclusions in these topics and have ample material on board here to dispute it. Nevertheless his criticism of Hume is one with which we agree, and which Skeptics would do well to heed: "...there are no a priori shortcuts. To reach any reasoned conclusion about miracles or any other past event, it is necessary to examine hypotheses about the past in competition with one another over the nest explanation that increases most the likelihood of the broadest scope of evidence. For all that we know, some divinity may decide to impress us once in a while with its feats of strength, and we may react rationally then by airing our grievances to it. In each case, it is necessary to examine the best explanation for the evidence, using fruitful theories about language, human motivation, and politics in traditional soceities to explain the broadest range of evidence." 
An added irony is that Tucker has apparently had encounters, as I have had, with what he calls "religious atheists" who view Hume as a sort of prophet and depend significantly on him for their worldview.
I should finally note that critics have appealed to a supposed defense of Hume against Earman, by Fogelin. There is not much to this defense. Fogelin spends all of 14 pages on Earman, and part of it is spent on summary of Earman and objecting that Earman describes Hume in unflattering terms (though apparently Fogelin has no problem with Hume calling people ignorant and barbarous). Another part is spent on expressions of gratitude that Earman didn't commit certain mistakes found in other critics of Hume. Then more space is spent agreeing that if Earman is right about what Hume argued, then Hume is dead meat.
Finally, Fogelin gets to actual defense, and his response runs down to claiming the Hume didn't really mean what he said. He admits Hume made "strongly stated conclusions"  and then makes all manner of rationalizations for why Hume didn't really mean what he said. In the end it is clear that what he finds are places where Hume qualified his strong statements precisely because he was at a loss to defend them as stated. In short, it demonstates the every "abject failure" Earman found in Hume, and which Hume himself had to admit to.
All Fogelin shows us in the end is that Hume had committed himself to an indefensible position which he found himself forced to qualify after criticism, and ends up trying to blame Earman for taking Hume at his word when he made his conclusions.
All Hume quotations are from An Inquiry Concerning Human Understanding.