While I agree with a lot of Zeltik’s choices and comments on “where songs originated”, I had two comments on what I didn’t agree with.
First off is a bias with Links Awakening, where I’d say Tal Tal Mountain is a more widespread and iconic song. The bias is due to a remix of that song being how I got into video game remix music and Zelda Reorchestrated (ZREO). I don’t recall the exact song I found on that old MySpace-adjacent Playlist site, but one of the classics is for sure this OCRemix track:
Secondly, for Breath of the Wild I’d say the (non-game) 2017 Presentation song is far more iconic than any of the games actual music. It even got included in Smash Bros Ultimate as remixed stage music! I think more people heard that song than any of the music found in the game. I know a number of people that never even tried to approach Hyrule Castle in their play through.