Hmm...

Here's a list of songs that you folks have already mentioned that are also on my list:

Lorena
Ashokan Farewell
Midnight On The Water
I'm So Lonesome I Could Cry
Angel
Skye Boat Song
Wayfaring Stranger
Scarborough Fair
Jesu Joy Of Man's Desiring
El Condor Pasa
The Boxer
Ne Me Quitte Pas
La Vie En Rose
Hallelujah (Leon
Dodi Li
Torna A Surriento (Come Back To Sorrento)
Yesterday
Shenandoah
Barbry Allen
Sheebeg & Sheemore (Hills Of Haversham)
The Minstrel Boy
O Mio Bambino Caro
Un Bel Di
Bring Him Home
Polovetzian Dance #9 (?) - Borodin (Stranger In Paradise)
Tecumseh Valley
Angel Band
Hallelujah! (Leonard Cohen)

Some that I would add are:
Con Te Partiro (sung by Anrea Bocelli)
To Where You Are (sung by Josh Groban)
The Prayer (Andrew Lloyd-Weber)
Brahms's Violin Concerto In D Minor (I think it's violin) - very moving and haunting main theme
Silkie (as sung by Joan Baez)
Take This Waltz (Leonard Cohen)
La Paloma
Blues In The Night (melody: Harold Arlen)
Over the Rainbow (melody: Harold Arlen)
Stormy Weather (melody: Harold Arlen
It Was A Very Good Year
Those Were The Days
Otchee Tchornya (Dark Eyes)
Rozhinkes Mit Mandlen (Yiddish lullabye)
Erev Shel Shosanim (Israeli folk song and dance)
Samba De Orfeo (from "Black Orpheus")
Manha De Carnival (from "Black Orpheus")
Windmills Of Your Mind
Forbidden Games (I forgot the older melody this song is se to)
Sheherezade main theme
Memory (Grizabella's song from "Cats" -- Lloyd-Weber)
Black Is The Colour Of My True Love's Hair
Home On The Range (I don't care if it's overdone, it's beautifully hauntine)
Londonderry Air (ditto)
La Paloma
High Barbary
Farewell to Tarawathie
Haul Away, Joe
Rollin' Down To Old Maui
Greensleeves (How could we forget?)
Louie, Louie - §;-D
Star Of The County Down
Bridget O'Malley
Blue Bayou
Gulf Coast Highway (James Lee Hooker & Nanci Griffith)
Spooky (Well, it IS haunting!)
Sakura (Japanese "Cherry Blooms" song)
In My Life (Beatles)
Here, There, & Everywhere (Beatles)
Blackbird (Beatles)
Kiss From A Rose (Seal)
The Rose (Amanda McBroom)
Now Is The Hour (Maori melody learned by Allied forces in WWII)
The Rebel Jesus (Jackson Browne)
Anathea (as sung by Judy Collins)
Lo, How a Rose E'er Blooming (Es Ist Ein' Roz' Entsprungen)
Geordie (as sung by Joann Baez)
Mountains O' Mourne/Bendemeer's Stream
Loch Lomond
Mo Mary
Bridge Over Troubled Water
Stardust
Isle Of Innisfree (Richard Farelly)
Do You Love An Apple?
Tumblin' Tumbleweeds (Bob Nolan)


That oughta fill up my iPod for a while. §:-D