Earlier this summer, I sat in on a couple of sessions of a reading group on ontology, in which one of the texts we examined was Sidelle's argument for essentially Carnap's view. Carnap thought that the ultimate questions of what things exist depend on how you want to talk about them, and which way of speaking about things was to be preferred was a purely practical question. It seems such sensible views are on the ascendant, at least if the conference Chalmers reports on is any indication. Chalmers himself apparently advocates a Carnapian view of ontology, and was apparently not alone at the conference. If only his views on the philosophy of mind were so reasonable.
The only rival view which I think is anywhere close to being as tenable is universalism, which allows unrestricted mereological composition. What that means, for the non-philosophers, is that any two things considered together constitute a third thing. There is a thing which is my left toe plus one of the electrons running through my computer as I type this plus the moon. No combination of things is too gerrymandered to count as a further thing according to universalism. Of course, we rarely talk about absurdly gerrymandered things except when giving examples to explain universalism, but I don't know how serious that flaw is. David Lewis, among the most prominent universalists, explained away this sort of problem by saying that normally we speak with restricted quantifiers; when we talk about what things there are, we're almost always talking about what relevant things there are, so the fact that we wouldn't ordinarily refer to the mereological sum of two apples on a table as a third thing on the table doesn't mean it isn't there, only that we don't normally consider it relevant.
Since there is indepedent evidence that we restrict quantifiers a lot (one of my favorite examples from Lewis: "all the beer is in the fridge" can frequently be used to say something true, even though it's never been the case that all the beer in the world has been in any particular fridge, because we immediately understand that the 'all' is being restricted to the relevant beer, perhaps the beer brought for the party), I think it's reasonable to appeal to restricted quantifiers to resolve problems. However, once this move is made, I don't really see a whole lot of difference between the Carnapian view and the universalist view. Of course, believing that you can adopt whichever view you like is adopting the Carnapian view, so unless there's a difference I'm missing Carnap presently wins this debate for me, but only by a narrow margine.