If I remember correctly, one of my favorite songs came out in 1995, Waterfalls by TLC, which also happened to be the second biggest hit of the year. Should someone in the story do something totally self-destructive and die because of it, it'd be a good one to add.
Edit to add: I suppose a link to the song would be good. http://www.youtube.com/watch?v=m-n-jZJhpT4
Also, Sheryl Crow's debut album came out in 1993. Several of the songs were released in 1994, and there are some memorable ones like "All I Wanna Do", "Strong Enough" (Are you strong enough to be my man <hint, hint>), and Leaving Las Vegas. *sigh* It seems so long ago. It so reminds me of younger days thinking about such music. Oh, and 1994 was when Madonna's songs "Take a Bow" and "Human Nature" came out... such awesome tunes!