The greatest (e.g., singer(s)) in {the world, the United States, the universe, the village, Toronto} ...
The greatest (e.g., singer(s)) on {television, the internet, radio, tour, the planet, Earth} ...
The greatest (e.g., singer(s)) of {these, them all, the Americans, America, the bunch} ...
The greatest singer in the United States implies she is living there (even if born elsewhere and/or out of country on a tour), while the greatest singer of the United States (not as common a saying) suggests that she was born there but now lives elsewhere or that she was the greatest singer in the U.S. until she was surpassed or died. It is more common to use "The greatest singer the U.S. produced {is, (until 2000) was} ...