In the West learning by ear is associated with traditional and folk music, but many classical music forms throughout the world lack notation, and have therefore been passed from generation to generation by ear.
The Suzuki method of teaching music focuses on playing by ear from a very young age. In his book "Teaching from the Balance Point," Edward Kreitman, a US based Suzuki Teacher, clearly distinguishes "learning by ear" as a separate, completely different process from "learning by rote".