The music of Nino Rota and Carmine Coppolla is one of the reasons these films were so great.
My favorite theme is Michael's theme and the original Hollywood music. If you have the DVD collection bonus materials you can listen to a recording of Rota's work and it sounds even better than with the orchestra in the films.
Also in GF2 the scene when Genco and Vito are watching a play, I love the opening music in that scene, it reminds me of the music that opens the wedding scene, and both really make me feel like a Sicilian immigrant. Its a strange feeling but i love those tunes. And in GF3 when anthony sings, thats a gem in that film, you can really feel the angst of people in Sicily and see the beauty of the countryside, you can see apollonia...well anyway.