What are the most significant responses to David Lewis' book On the Plurality of Worlds (1986)? In particular, are there any good critical readings of Lewis' views on modal realism?
Despite the popularity and impact of Lewis' On the Plurality of Worlds, the two given answers are really bad. So here I try to give an overview of responses to Modal Realism.
Modal Realism proposes to read modal statements in possible-world-talk literally. It is an ontological theory, and it commits itself to a plurality of possible worlds. The reason to believe in it is utility. You can do a lot of useful stuff if you believe in a plurality of concrete possible worlds.
A bunch of criticism can be found in the Plurality itself, in chapter 2 and 3. Chapter 2 is looking more into problems and prima facie criticism. Chapter 3 deals with ersatzist positions. They claim that there is not a plurality of concrete worlds, but of abstract objects, that do all the job of Modal Realism without commiting us to an, arguably weird, ontology. Ersatzism comes in different flavours. Lingustic Ersatzism for example thinks that an ersatz world is a maximal set of consistent sentences. Pictorial and Magical Ersatzism gets mentioned in chapter 3 aswell.
If you look for things outside Plurality, check out:
Robert Stalnaker: Critical notice of D. Lewis, On the Plurality of Worlds. Mind (1988), 117-128.
John Divers and Joseph Melia: The Analytic Limit of Genuine Modal Realism. Mind (2002), pp. 15-36.
Scott A. Shalkowski: The Ontological Ground of the Alethic Modality. The Philosophical Review (1994), pp. 669-688. (especially section 2)
These deal with Modal Realism, and why it might be a bad theory.
For alternative views beside ersatzism mentioned in Plurality itself, I just want to drop some names:
There is Modal Scepticism (Melia: Modality ch. 3), Modal Fictionalism (Rosen: Modal Fictionalism, and Modal Fictionalism Fixed) and Modal Reductionism (Sider: Reductive Theories of Modality, sections 1-3) among, probably, many other.
I would have to agree with Cody's comment. I haven't read OPW, but did study his view briefly a few years ago. If I recall correctly, he effectively unilaterally proposes the plurality of worlds, and furthermore grants that the many different worlds that exist cannot, have never, and will never have even the slightest impact on each other. I think the reason people stare incredulously, like you say, is because there is hardly anything to say in response. There's nothing at all to refute, and absolutely nothing turns on Lewis being correct or not. Certainly it has an interesting parallel to modal language, but it's interesting in much the same way the personality a child ascribes to a stuffed animal is interesting - a curious thing to consider, but completely inconsequential, and hardly worth debating.
Although I dont know Lewis' book, the summary provided by wikipedia suggests that his idea is similiar to what has been discussed since the 50s as the many world interpretation, originally by Everett, of quantum mechanics. Prominent proponents of that interpretation are De Witt and Deutsch.
The failure to find a unique string vacuum has prompted some string theorists (Susskind among others) to claim that there is a "string landscape" and our universe occupies just one of the possible vacua. Whereas other universes might occupy different vacua at the same time.
Ideas of this kind had already been expressed before the appearance of Lewis' book, but became more prominent in the late nineties, since by then it had become clear, that it would most likely not be possible to find a unique string vacuum.
An article you might enjoy reading is Possible Girls. It discusses interworld romantic relationships.
I realize that this not really an answer to your question, but I think the usual objections to the many world interpretation of quantum mechanics can be raised against Lewis.
As has been noted, modal realism is a proposal that is not intended to be supported by observation. Instead, it is meant as a theory that explains, unifies, and performs other tasks for which theories are developed. (As one other respondent as said, it attempts to take the talk of possible objects literally.) The motivation for doing this is out of, for one thing, simplicity--which is a theoretical virtue. The meanings of expressions would be very unambiguous, under Lewis's proposal. In theories of modality that compete with modal realism, one always has to give a very complex and contentious story about what, exactly, they are suggesting modality is.
Another reason that motivates modal realism is, as opposed to some other theories where abstract objects are given some kind of elevated ontological status, modal realism has a kind of "ontological parsimony" in that the only objects in the theory are physical objects.
One final thing is that you can, to some extent, see modal realism in a different light: Think of it as making the point, "Why should you believe that everything that exists is spatio-temporally connected? That is a theory that comes bundled with a superfluous metaphysical commitment. Modal realism is entirely consistent with relaxing that commitment." Of course this doesn't get you to the conclusion that every conceptually possible, spatio-temporally disconnected region exists--but it does, perhaps, make it seem much less astonishing to suppose that they do.
Now having enumerated some motivations for modal realism, you can perhaps see how people might argue against it: You may attack the motivations. Some argue that modal realism is not superior in its simplicity to some other competing modal theories, or they say that it is not sufficiently simple in comparison to make up for its theoretical vice of grounding all modal language in objects with which we have no contact. Others would argue that it is not as ontologically sparse as it claims to be since, although it can handily do away with abstract objects as well as any theory can, it still proposes far more physical objects than are necessary.
If a modal theory can retain the feature that only physical objects exist, be adequately simple, and still not excessively violate desired features of our language, then this would be a devastating blow to modal realism. However, nobody has presented a theory which has convinced a large majority of philosophers that it has these features.
Still, the general consensus seems to be: Yes, you may gain a lot of theoretical virtues by accepting modal realism. But those theoretical virtues simply cannot adequately compensate for all the vice that comes with them.