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It sets the tone for the game, areas, characters, and encounters. The music fills in all the cracks and blank spaces and fleshes out the game.
Music also acts as a sponge that soaks up all your great memories of the game and brings them back to you every time you listen to the songs again.
http://www.youtube.com/watch?v=aQx9QaAxhk8Video Game Music is just that, Video Game Music. It is designed for a specific purpose, to fit a specific part of the game, it isn't designed just to sound beautiful, its designed to evoke specific emotions and thoughts and be the backdrop to very specific actions and encounters. THAT is what makes Video Game Music so important and special.
When you hear any song from Chrono Trigger you remember exactly where that song was played and all the wonderful moments you experienced, when you hear Aerith's theme you can feel that dropkick to your heart...