A short time ago, I was asked to help a patron who had come from out-of-state to the Brigham Young University Family History Library with some genealogical research in the Philippines. I immediately accepted the opportunity because I simply assumed that FamilySearch.org likely had a large number of records from the Philippines for the reason that The Church of Jesus Christ of Latter-day Saints has a large number of members in that country.
I was not disappointed. There were a great number of records and I soon found some crucial ancestral names for the patron. The patron was obviously very happy. But what about finding records on the FamilySearch.org website from countries where there are few members of the Church? I learned from some of the other missionaries at the BYU Family History Library that the website had a large number of very useful records from India (see the screenshot above).
Then I got interested to find out what other countries, outside of those usually associated with genealogical research, might be represented by records on the website.
One key to answering the question is to start any search by using the FamilySearch.org Catalog rather than simply looking at the list of digitized records available in the Historical Record Collections. For example, there is a huge list of records from Italy.
Granted, there are still places around the world where genealogical records are not easily obtained, but before you make such a conclusion, I would suggest that you do extensive online searches. The FamilySearch.org website has more than a hundred year's worth of accumulating records and I would not discount the fact that some records may have been obtained that are pertinent to most of the world's population.
Another example comes from China. It seems that many researchers automatically assume that Chinese records are not available. However, FamilySearch has a huge and rapidly increasing number of records from both China and Taiwan. Here is a representative screenshot.
You will never know what you are missing until you look. One last example. This one is from Africa.
If you keep clicking down in the places included links, you will see additional resources, but you can also search by looking for a specific country.