Another place you can find some beautiful & haunting melodies is in the "Dragon Quest" series in the form of symphonic suites, composed by Japanese composer Koichi Sugiyama. The DQ series was/is a popular game series in Japan, but was much less successful internationally, being known as "Dragon Warrior"... however the music is also legendary in Japan. Drawing from the styles of composers like Tchaikovsky, Stravinsky, J.S. Bach, Mozart and even John Williams in addition to Japanese contemporaries, Sugiyama has created soundtracks to 9 games so far in the series (spanning 25 years). Once you hear some of the music that has come from this series (if you enjoy orchestral music), I think you'll understand why it is so loved by those who are familiar with it.
Here are a few of my favorite haunting melodies from the series:
"Requiem" - Dragon Quest II - a very sad, but pretty melody
"Heavenly Flight" - Dragon Quest III - one of the best pieces from the entire series IMO - gorgeous melody
"Distant Memories" - Dragon Quest III - the cello sings in this piece; another sad melody that exudes a sense of longing
"Homeland / Wagon Wheel's March" - Dragon Quest IV - I love pieces that make you feel like you're traveling and this is one of them, both in the melody of the first section and then in the insistent march rhythm of the second section
"Battle For The Glory" - Dragon Quest IV - grand and epic, a feeling of danger is pervasive here - the later section is the most haunting part - could easily be something out of a film soundtrack
"Magic Carpet / Ocean" - Dragon Quest V - although there are only a few minor chords in this piece, there is a hauntingly beautiful melody here
"Monsters In The Dungeon /Tower Of Death / Dark World" - Dragon Quest V - an unusual but interesting melody - despite being somewhat lively, still haunting
"Noble Requiem / Saint" - Dragon Quest V - a lovely piece - pretty, but very dark in tone
"At The Palace" - Dragon Quest VI - a very Baroque arrangement here
"Ocean Waves" - Dragon Quest VI - another beautiful piece with a unique melody
There are many other really nice pieces from the series... awesome character themes, great town & castle themes, some exciting battle music, etc. If you like what you hear here, I encourage you to check out the symphonic suites to all the Dragon Quest games... a lot of which you can find on YouTube. You just have to ignore the original game soundtrack, which is not nearly as interesting to listen to on its own (although fun to compare to the symphonic versions!)