There has been some buzz in the blogosphere about this paper, which in the press and on blogs has usually been described as predicting the extinction of religion in nine countries. So I thought I'd put in my two cents.
(1) Saying that the study predicts the extinction of religion is somewhat misleading; what it predicts is the extinction of religious affiliation. On the account of 'religion' being considered, someone who believes in God, prays every day, and attends church every Sunday (but not as a member, only as someone looking for a church to attend) could count as not being in the 'religious' column. Likewise, many people who count as non-religious under this sort of definition believe in God, pray, etc.; they just don't attend church or anything like it. We also have to keep in mind that religious affiliation is not hard-and-fast (people are often in transition states) and have been known on occasion to hide their actual affiliation or affirm an affiliation solely due to social pressure.
(2) Obviously the conclusion that religious affiliation will go to zero is so historically and sociologically improbable, particularly given factors like immigration, that the conclusion really should be understood to be qualified by "if no significant countervailing factors arise." (The authors are quite above-board about the fact that they are abstracting from things that could have real effect -- this is an 'assume a cow is a perfect sphere' sort of exercise, to get an idealized model that is at least reasonably close to serve as a starting point for further work.) That there can be significant countervailing factors is clear enough from history; it doesn't follow, of course, that they are always operative in sufficient strength to make a difference.
(3) The key assumption, that perceived utility and size of population are significant factors in the decrease of religious affiliation, is very plausible. Both factors, perceived utility and size of population, clearly do have an effect on religious affiliation, which is why laws, for instance, can have an effect on religious affiliation by increasing or decreasing the benefits associated with it or by affecting support of the population size by immigration. Almost everyone recognizes the effectiveness of these factors to some extent. (The history of the Catholic Church in the United States, to take just one example, consists in great measure of struggles over laws that were officially neutral but were nonetheless clearly designed to make it harder for Catholics to operate or immigrate, and indeed were often explicitly defended by their proponents as such.) Human beings are social animals; social value does have an effect on such things.
(4) Nonetheless, none of the nine countries presented as fitting the model is a hugely impressive choice: all nine are countries in which religious affiliation is already well-known to be declining. Thus it seems to me that even if the statistics completely checks out, the paper at most tells us that, of countries in which religious affiliation is declining, at least these nine fit a simple model in which decline is generated by perceived social utility and size. This leaves open any number of questions.
(5) I find it somewhat ironic, though, that the authors say, "For decades, authors have commented on the surprisingly rapid decline of organized religion in many regions of the world," given that for decades authors have also commented on the surprising tenacity of organized religion in many regions of the world. In actual fact this paper doesn't tell us anything fundamentally new; the data is already known (it's the only reason why the mathematics is taken to model a decline rather than a more symmetrical relationship) and people have proposed similar causal analyses for it before. All it does is provide one possible mathematical model for such a causal analysis. Indeed, the general point of the model is already widely accepted: that in a situation in which there is a choice of membership between two populations, then, ceteris paribus, circumstances favor the population that is larger and is widely seen to be socially preferable. One can well imagine that if the researchers had proposed a mathematical model for organized-religion-is-tenacious analysis, picking out countries where it already is known to be tenacious and showing that they fit the model, that some of the paper's current critics would not be so critical and some of its current enthusiasts would not be so enthusiastic, especially if the press reported it as an argument that religion was here to stay.
(6) It was a cool idea to try to develop, regardless; and I hope more work of this sort is done.
(7) All of the above is very quick and rough.