1. Ohhh! very important! For me it isn't a cruicial part of the gameplay, but a good piece of music definitely helps you "live into" the game and generally deepen your gaming experience.
2. Yes, look at tetris. Altough no music would be booring in itself, it wouldn't change tetris' playability much. The music only gets on your nerves anyway when you have nearly lost, it get's really fast and counter-productive to say the least.
3. I can't name one game as i hold atleast 3 very much on 1st place. Unreal: the great atmospheric music really enhanced this game. Wouldn't be the same game without it. Final Doom (for PS1): It had some very neat ambient tracks that made this Doom a very different game than the other early Doom games, which had midi tracks. That difference really showed what music can do. I actually remember i was afraid to play the game because the music freaked me out. The Dynasty Warriors games: Consists of electric guitars and still manages to keep this old-chinese style with the flutes and drums. Very neat.
Sorry if the answers were to long...
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