In Zelda 3. When you get excalibur for the first time !

https://www.youtube.com/watch?v=5saXnUkPzMY

All KH

The entire Golden Sun franchise hits me good.

I'll stick to only one track for each games, but there are more than one theme for each that could make my list:

And finally, I'll include this amazing rendition by the Distant World Orchestra, just because:
 
  

being 33 years old i have alot of nostalgia from videogames from the 90's and its the soundtracks that really bring on the nostalgia emotion. I played loads when i was younger, But i just love the Donkey Kong Diddys quest soundtrack, i could listen to that over and over and constantly have a really happy feeling about those good times going round my friend Joanna's house with my bro and sitting playing that game.

Dark Cloud's Main Theme

Dark Cloud 2's Neverending Adventure and Time is Changing

Level 5 give me Dark Cloud 3 pls!

Any track from Donkey kong 64, but specifically this one:

https://www.youtube.com/watch?v=bp_fCUnna0A

This one easily, or a few others from the same game

https://www.youtube.com/watch?v=ko3FwIgIVoc

End theme of xenosaga part III, was really an emotional moment

Pretty much any song from Undertale or the N64 era Mario games. Rainbow Road and Staff Credits always get to me. The ending song to Sonic Adventure 2 still holds incredible emotional value for me, and the Mother 1 ost made me feel nostalgic for a game that I don't have any memories of. Oh, and the Duck Tales Moon theme is fucking magical.