I wanted to take time to write concerning the demographics of the Church and what Church Leaders have said concerning its status internationally. President Hinckley and other General Authorities have in recent years declared that the Church's demography is spread all across the globe. President Monson stated in the past week in a press conference, "How grateful we are for the dedication, the faith and the strength of the people of this Church who now number more than 13 million in 176 nations and territories throughout the world. Our membership continues to grow steadily." Clearly the Church has spread itself accross the majority of the countries of the world. However, Church membership is by no means evenly distributed across the countries of the world.
Now for some statistics. A little over 84% of Church membership resides in North and South America (including the Caribbean) and almost 86% of the Church's stakes. Out of the 125 currently operating temples, 31 are outside of North and South America. The Church has established itself in every country in the Western Hemisphere (excluding Cuba) and the Southern Hemisphere (except East Timor, Rwanda, Burundi, The Seychelles, and Comoros). In Europe, the Church has a presence in every country except Macedonia and Bosnia (from what I have found).
This post is by no means criticizing anything Church leaders have said, but rather I am making a point that although we do have members residing in most of the countries of the world, most of the members live in the Southern and Northern Hemispheres. Something I have found interesting is how well the Church has grown in island nations. For example, the country in Africa with the highest percentage of members is Cape Verde and is around 2% and the country with the second highest is less than 0.2%. The countries which have the highest percentage of members are island nations concentrated in the South Pacific like Tonga (46%) and Samoa (36%). The Church has grown the most in Europe in the British Isles with over 100,000 members more than the country in Europe with the second most members (Spain with around 41,000 members). The Philippines has the most members out of any of the countries in the Eastern Hemisphere with around 600,000. I believe this is a fulfillment of prophesy in 1 Nephi 19:16, "Yea, then will he remember the isles of the sea."
Here is a list of all of the countries in the Northern part of the Eastern Hemisphere with no Church presence. I define this as meaning no branches established and no membership reported. Countries in italics means that the country is predominantly Muslim (which tend to not allow other religions to proselyte or publicly practice).