In older games sometimes the musical soundtrack was in fact, natural sounds. If you get the original Fallout, it has a few tracks of music, and then quite a bit of almost nothing but nature, like wind blowing in the irradiated desert. Sometimes minimal music is better than no music.
I'll have to give New Vegas a shot without music, at least once I hear it all. I find the musical selections of that era used in the games pretty interesting.
Music in older games was filler, because the lack of noise would seem just wrong, so they tried to go for basic themes. Imagine Super Mario Brothers without any music at all. Imagine the Legend of Zelda without any music at all. The music was put there to make a good game great. Some developers forgot that music isn't a requirement for a game. If done correctly, it is a tool used to help players out. If done incorrectly, it can detract from a game. Silence is in fact its own style of music, and can both enhance and detract from a game.
When I think of how music both enhances and detracts from a game at the same time though, I can only think of Left 4 Dead. The music composing software is great, but it does get a bit repetitive, and it never shuts off. Sometimes I think some points in the game would be better without music. Picture the music shutting off when you're sneaking by a witch, the only things you can hear are your footsteps, and her breathing. I think it would freak you out more than any music they could add.