Here's an interesting map that shows the proportion of non-religious people by country:
https://upload.wikimedia.org/wikipedia/commons/f/f0/Irreligion_map.pngI think there is at least one mistake on the map - Azerbaijan is too dark.
However, we can get a pretty good idea of what places are very religious, and what places are very secular.
Very religious places include Africa, the Middle East with the exception of Israel, Southeast Asia with the exception of Vietnam, and some countries in Central and South America.
Very irreligious places include China, Vietnam, Japan; Scandinavia; Northern Europe from France to Russia, with the notable exception of Catholic Poland; to a lesser extent, Canada, Australia, and Southern Europe, not including the Balkans north of Greece and Bulgaria.
Here's an interesting article that asks the question, "Are Prisoners Less Likely to be Atheists?":
http://fivethirtyeight.com/features/are-prisoners-less-likely-to-be-atheists/The headline figure is that, atheists (a narrower category than the "irreligious" I discussed above) make up about 1% of the population of the U.S., and about 0.1% of the federal prison population.
So, on the whole, it seems that secularism is positively correlated with healthy societies and moral behavior.
Edited 12/2/2015 12:36:36