GSC has the best music, the best Pokémon, the best story, the best Rival (Silver), the best final boss ever (Red)...You see that team in my signature? That's my main fighting squad in Silver Version, which is by far my favorite in my whole collection!
As far as music goes, I particularly like the Rival's appearance theme, the Rival's battle theme (which I have affectionately dubbed "Preemptive Strike"), the Lucky Number Show, Buena's Password, Indigo Plateau, and Lance/Red's battle theme (which I have affectionately dubbed "Ultimate Challenge!").
I do have one question about the music, and it isn't restricted to Generation II: Why does the Rival always have better theme music than the player?!