Q. I am looking for a current list of third world countries.

Since the term "third world countries" referred to countries that were not aligned with either the United States or the Soviet Union during the cold war era, I do not believe the term is in use anymore.

Probably the closest current equivalent to that group would be countries that are below a certain level of economic development, but the term "third world" was meant as a political categorization rather than an economic one.