Here is some info from ever-wonderful wikipedia about the religious/sacred music of the main religions of the world. Whoever wrote it massively simplified the whole thing, but they seem like good starting points.
So here are the religions, with a link to the wikipedia article on their devotional music style. A lot of these just relate to specific styles associated with specific subsets of the religion. Its the best I could do at the moment.
Hinduism and Sikhism -
Kirtan
Judaism -
Sephardic Music (this one's actually just about Sephardic Jews, who are those around the Iberian peninsula - Spain etc. -, but the author though it was enough!)
Islam -
Islamic Music
Ah, now I'm bored... the rest of the styles are written about at :
http://en.wikipedia.org/wiki/Religious_music