food - In what countries is chalav yisrael not required for milk?

The Talmud says milk is not kosher unless a Jew supervises the milking, to be sure it's just kosher-animal milk.

Assuming one goes by the ruling of R' Moshe Feinstein and others that "knowing" is considered like "seeing", the combination of regulation and economics in the USA is such that we know that commercial milk is 100% cow's milk. (Okay there's added vitamins but they're batel, that's a different topic.) Hence we drink "chalav stam" a.k.a. "chalav hacompanies" a.k.a. "non-chalav yisrael" or call it what you will. (And those who drink only chalav yisrael usually accept R' Moshe at some level and treat their practice as a chumra [a chumra recommended by R' Moshe himself in many cases].)

In other countries of the world: Can you do the same? Or is traditional Jewish supervision required? In which countries?

This is a "moooot" point in Israel as there will be Jews working in the dairy farms; and theoretically you could have a country where the regulation and economics are there, but everyone follows the local rabbi who rejects R' Moshe's argument, though I'm not aware of any such place.