According to Wikipedia, "Music can be described in terms of many genres and styles. Classifications are often arbitrary, and may be disputed and closely related forms often overlap. Larger genres and styles comprise more specific sub-categories."
There are 4 primary music genres:
Art music (classical music): primarily includes classical traditions, including both contemporary and historical classical music forms.
Popular music: any musical style accessible to the general public and disseminated by the mass media. Sub- categories include "Country", "Blues", "Hip Hop", "Jazz", "Rock", etc.
Religious music: performed or composed for religious use or through religious influence. "Gospel", "spiritual", and "Christian music" are examples of religious music.
Traditional and folk music: traditional music are songs and tunes that have been performed over a long period of time (usually several generations); folk music is orally passed from one generation to another.