Basically, the upshot is this: although, there is some small variation withiin the "developed" world (ie Europe, Japan, South Korea, USA, Canada, Australia, Taiwan, New Zealand) vis-a-vis demographic "futures" (Australia, New Zealand, France, and the US on the higher end, Italy, Germany, and Japan on the lower end), all of these countries have a birthrate between 8 and 14 per 1000 per year (as of 2005). The real gap lies between the "developed" world and the "developing" world, which has a much, much higher birthrate, whether or not the country in question is predominantly Muslim or Christian (or otherwise - indeed, as a side note, I think the explosive population growth in the non-Islamic world is vastly underappreciated in much of the current debate, as is the rise of various syncretic forms of quite fundamentalist Christianity, especially in Africa). The countries above 14 but below 20 births per 1000 tend to be nations that are "rapidly developing" or have economies and middle classes significantly larger than typical "third world" nations, but still substantially poorer than the developed world (ie Brazil, Iran, Argentina, South Africa, Turkey, maybe Ireland (although I think Ireland has largely "graduated" into the "developed" category)).
The following list tries to be comprehensive, although not exhaustive. I try to include every important country in the world, as well as several nations from each global region and subregion - ie Africa, but French West Africa, the Maghreb, Southern Africa; or Europe, but the Meditteraenean, Scandanavian, and the former Eastern Bloc.
Below is a list of these birthrates (number of births per year per 1000 inhabitants), derived from the CIA's "World Factbook," and listed in ascending order:
Czech Republic, 9.1
South Korea, 10.1
United Kingdom, 10.8
China, 13.1 *
United States 13.9
New Zealand, 13.9
Israel, 18.2 #
South Africa, 18.5
Dominican Republic, 23.3 &
Saudi Arabia, 29.6
Guatemala, 34.1 &
Cote D'Ivoire, 35.5
Democratic Republic of the Congo, 44.8
I think what this list demonstrates is that - as demographers, sociologists, and economists have noted extensively - the greater the poverty in a nation, the lower the level of education (ESPECIALLY the lower the education levels amongst women), the higher the birthrate. Thus, we should not be surprised that the countries with by far the highest birthrates are from the world's poorest region, sub-Saharan Africa, followed by some of the poorer nations in the near East, like Iraq and Syria. While I do think religion is a factor in higher birthrates, it is incidental and not catalytic - ie nations that are poorer and have lower levels of educational attainment also tend to have much higher levels of religious fervency (which, it should be noted, is not necessarily the same thing as religious observance, which can be simply a social custom rather than a vivid reality). Again, these tendencies are not monothilically true: obviously, factors such as governmental policy can have a significant impact - see the "pro-natal" policy effects on certain European nations, the relationship between the transition away from Communism and lower birth rates in the former Eastern Bloc (even in still quite pious nations like Poland), the effect of extensive and long-standing government policy to limit the birthrate and Chinese.
But nevertheless, I also think this information tends to suggest what the "Eurabia" crowd (including Mark Steyn are): paranoid, bordering on delusional, this generation's version of the John Birch Society: only now the menace is "green" (Islamic) not "red," and the conspiracy is a secret Muslim Brotherhood plot to take over the governments of every European nation, not a secret cadre of communists within the US Departments of State and Defense.
* on China, clearly the "one child" policy has significantly altered the nation's birthrate.
# on Israel, I am not sure if this number includes the West Bank and Gaza or not. Even if doesn't, I think the fundamentally precarious nature Israel finds itself in suggests that a series of demographic and physical pressures exist on the society that would tend to work against what the educational and economic data would suggest Israeli demography would be like in a different geopolitical context.
& The Dominican Republic and Guetamala are included because they - along with Mexico and Puerto Rico - probably represent the most significant sources of immigration to the United States and the United States's concomitant "Latinization." Also, neither country is "small": Guetamala currently has a population of over 14 million and the Dominican Republic has a population of close to 9 million. Considering how small these countries are - especially the Dominican, which shares the island of Hispaniola (smaller than Ireland, geographically) with Haiti, itself with a population of 8 million - these trends represent a kind of irresistible migratory pressure. Indeed, Latin America should be seen as playing a similar role vis-a-vis labour supply and immigration that the Maghreb, West Africa, and Turkey plays vis-a-vis Europe's economy and demography.
An Addendum on the "Latinization" of the United States
Furthermore, I would argue - from my personal experience, both travelling and as a scholar of 20th century US history and urban geography - that the "Latinization" of the United States is a considerably more significant trend than the various third world/post-colonial migrations to Europe. Really, you have to go to south Florida or Southern California to see what I mean. Essentially, an alternative Spanish-speaking socio-cultural world exists in Florida, California, Arizona, Texas, and Nevada in particular - with extensive Spanish language media and large business districts with signs in Spanish, even at public schools. From personal experience, I can tell you that anywhere from a quarter to a third of the radio stations in the LA/Orange County/Inland Empire/San Diego region are Spanish. In the Miami area, there are at least 8 or 9 Spanish language channels on cable, offering music video shows, news, televangelism, game shows, talk shows all in Spanish. However, it should be noted that the Latino presence in Florida is of a considerably different nature from that in California: really, Latino Florida is of the Caribean basin (Cuba, the Dominican, Puerto Rico, Panama, Columbia, Venezuela), while that in California tends to "Aztec": from Mexico, Guetamala, and El Salvador - and there are significant cultural and historic differences between the two diasporas (which I will perhaps elaborate on in the future.