Here's a few great examples:
Mother 2 from Earthbound. https://www.youtube.com/watch?v=_e_GqFqq0_w
Sounds like an opening to an Anime, but it's one of the most upbeat and happy songs I've probably ever heard, quite amazing in fact.
Battlefield: https://www.youtube.com/watch?v=eNs5ei6xUhM
My memory is a little foggy on this one, but when you were doing Multi-Man Melees or story battles with a certain character this would play later on on a certain stage.
Poke Floats: https://www.youtube.com/watch?v=xxdTM2GB2PM
Classix medley of several great Pokemon themes like the Trainer Battle, Gym Leader Theme, and Wild Pokemon theme.
Fountain of Dreams: https://www.youtube.com/watch?v=0wLoirmq8MU
Amazing Orchestra arrangement of one of Kirby's most well-known themes.
Fire Emblem: https://www.youtube.com/watch?v=HjRmdwGILfc
The classic Fire Emblem theme, with some nice touches.
Targets: https://www.youtube.com/watch?v=TXHQb7RN9lE
Even though the Target Practice mini-games could be infuriating sometimes, at least the music is catchy.
Big Blue: https://www.youtube.com/watch?v=9ZLi13Yk358
From F-Zero, I never played the original, but this re-imagining of it is amazing. The Mute City version is also out there as well.
Final Destination: https://www.youtube.com/watch?v=UvfDISoyvWk
Oh Master Hand...What a pain in the ass you could be. I like Brawl's version better, but this one is still superb.
There are tons of others from this Youtuber, all extended to 30 minutes, check them out when you can.
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Melee had great music. I remember being subscribed to Nintendo Power and one of the issues came with a CD with all the music in an orchestral form.
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What does eyesight have to do with sound?
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Interesting...