I think that you can go with this in several different ways. In terms of the 1990s, I am not sure one can go very far without discussing the influence of Grunge music and the Seattle scene. The fact that music underwent a time when fashion and superficial image was not the driving force behind music is something that impacted the time period tremendously. At a time when the 1980s had fully passed, when economic recessions and contractions had changed the view of many in the social setting, and when greater understanding about cultural differences emerged, grunge music captured the music scene's attention. The songs coming out of this time period were about alienation and topics related to personal estrangement from a social order. When Eddie Vedder writes in marker "Pro- Choice" on his arm during a Pearl Jam music session, it indicates a fundamental shift in music. The leaders of grunge were fundamentally uncomfortable with their success and the commercial exploitation of artistic message. This helped to explain why the grunge musical scene was a bit more than just music, for in its purest form, it was one of the last times we see musicians openly suggest that "being famous was one of the last things" desired, to paraphrase Kurt Cobain.
This would depend a great deal on what kind of music we are talking about. It is also completely a question of opinion because we cannot know for sure that a certain change in society has actually been caused by the music that is present in the society at the time the change occurs.
You can find many people who argue that rap music has contributed to a coarsening of our society in the last couple of decades. They will point out that, for example, the use of words that are derogatory towards women (as well as their videos) have made people see women more as sex objects than was previously the case. There are also those who would argue that rap has helped make society more violent because it glorifies violence.
Again, this is purely opinion because there is no way to actually prove that rap, rather than other things, has caused any changes that have happened in our society. There are studies that have attempted to show a connection, however. I have included a link to one below.