Frank, I have never seen a Mexican cheese, other that the shredded Taco cheese or some Jack Cheese with chopped jalapenos in it. So I have to respectfully disagree about nadin's homeland cheeses.
Mexico makes GREAT cheese. In most markets they have huge cheese cooler sections -- frequently an island with probably 200 or 300 cheese and in the middle they cut it from the wheels.
You can also go to some cities where the cheese is hand-made in smaller batches.
My favorites are Manchego, Chihuahua, Panela, Oaxaca. They are very flavorful. American style cheeses, even sharp cheddars, just don't have the depth of flavor. Also, the American versions of those cheeses lack flavor and depth as well.