I know this is an old thread...but being a tune person myself, I often relate to instrumentals instead of songs with words. I often like various opera arias where I don't even understand the words. Somehow the emotion is expressed in the tune.

Un Bel Di (One Fine Day from Madama Butterfly)
Vissi d'Arte (from Tosca)
Prelude to Act III (from Carmen, sounds like The Minstrel Boy)

and then all the melancholic Scottish tunes...(the ones I like to play on the piano when the electricity goes off ;-))
Ye Banks and Braes (Bonnie Doon was mentioned above)
What Ails This Heart Of Mine
Rare Willie

and then most of Chopin...
Ballade in G (I'm Always Chasing Rainbows - the words spoiled it IMO)

the second movement of Beethoven's Pathetique Sonata (I loved it before I ever heard Carl Haas use it for the theme music to his program.)

and that gorgeous 18th variation on a theme of Paganinni by Rachmaninoff (was it used in a coffee commercial?)

what about Max Bruch's Scottish Fantasy where he uses the Scottish folksongs "I'm a Doun for Lack o' Johnnie" and "Thro the Wood Laddie discussed at Mudcat here and here.

Lonesome EJ - I love the waltz that follows Copland's Corral Nocturne. It is really "I Ride an Old Paint" with a different rhythm (my opinion).

Julia - I guess you know that "Music of the Night" from Phantom is the same opening interval as in "Come to Me, Bend to Me" from Brigadoon.

Peter T - you once mentioned "Humming Chorus" from Madama Butterfly. It's the same as "Bring Him Home" from Les Miz. Also, you mentioned above about moments inside melodies - how about the anticipation in Copland's Waltz - where you are waiting to start the tune/emotions and just lean into it as it finally starts!

clj (from way back in '99) - if you like Scheherazade, by Rimsky-Korsakov, you'd also love all the Polovtsian Dances by Borodin, another Russian. (made into popular tunes in the musical Kismet... Stranger in Paradise, And this is My Beloved, etc.)

But I still like the tunes without the words.