I have questioned this within myself as well, but now I just enjoy. Music touches the soul in many ways, depending on the style.
Although not religious at the time, while in Vancouver, I took my daughter to see the Vancouver Symphony's Easter concert at the Orpheum, it was incredibly beautiful! I saw it as a beautiful Art and Cultural experience for her to enjoy as well as myself.
I adore Ave Maria, I too always feel incredibly emotional when I listen to it.. shivers run through me. Another beautiful fave is The Prayer done by Andrea Bocelli and Celion Dion...
Hope its ok to share a link to these songs:
Ave Maria http://www.youtube.com/watch?v=2uYrmYXsujI (gosh how can anyone not feel the beauty of this)
The Prayer http://www.youtube.com/watch?v=db1-IlnW2YY