Actually, he had about a dozen different sound he made through the years, including grunts, screams, and growls.
His famous "SKRRRREEEEEEEEOOOOOOONNNNKKKKKKK!" call has evolved through many different incarnations. Like his appearance, its sound was based, in large part, on his "personality" in the particular movie he was in.
In the first "Godzilla", it was deep, powerful, and resonated. It well-suited the ambience of fear in the movie. For films in which he was "the Good Guy", it was of a higher, less-threatening pitch. Godzilla actually had a pretty good vocabulary.
It wasn't even a real animal's roar, either. It was created by Akira Ifukube, the longtime composer of the Godzilla series (who was responsible for Godzilla's theme-march), by rubbing a resin-coated glove along a contrabass and amplifying it. Certainly, that simple effect became one of the most recognizable sounds in movie history, never equaled.
Google "Godzilla roar .wav" for a LOT more sites and sounds. I figure this thread could use them!