I haven't watched all these videos but to determine they play the song I'm intending...
Here are some that I use as lullabies (varying depending on my mood):
Theme from Missing by Vangelis
YouTube - Vangelis - Missing
The Kiss from Last of the Mohicans score...
YouTube - The Kiss - Last of the Mohicans Theme
Gutter Glitter by Switchblade Symphony (apparently people like to tribal/belly dance to this one)
YouTube - Mariangela Demurtas
Bloody Knuckles...
YouTube - Switchblade Symphony - Bloody Knuckles / Gothic
Farewell and Goodnight by The Smashing Pumpkins
YouTube - Farewell And Goodnight - Smashing Pumpkins
Cupid de Locke...
YouTube - Smashing Pumpkins - Cupid De Locke
Scarborough Fair/Canticle by Simon and Garfunkel
YouTube - Simon & Garfunkel - Scarborough Fair/Canticle
I can't find the album version of this sadly... but Dear Daniel by Ruby Throat
YouTube - Ruby Throat (Daniel and the lions)
Millenia by Rhett Brewer
YouTube - Hotel de Ville: Millennia
Kabe Habe Bolo by Rasa
YouTube - SHIVA PRIYABHAKTA
Gopinatha...
YouTube - Gopinath, a prayer of Srila Bhaktivinoda Thakura (bengali ; english lyrics)
The Mystic's Dream by Loreena McKennitt
YouTube - Loreena McKennitt - The Mystic's Dream
Dante's Prayer...
YouTube - LOREENA McKENNITT - Dante's Prayer
Night Ride Across the Caucasus...
YouTube - Loreena McKennitt Night Ride Across the Caucasus
Gates of Istanbul...
YouTube - Loreena Mckennitt - The Gates Of Istanbul
Waka in the Sky by Lisa Gerrard. I assume it's looped or something because the song is only like 1:41 long.
YouTube - New Zealand a dream
Long, Long Time Ago (Lullaby from Pan's Labyrinth) by Javier Navarrete
YouTube - Pan's Labyrinth Song
Watermark by Enya
YouTube - Enya - Watermark
On Your Shore...
YouTube - Enya - On your Shore
Exile...
YouTube - Enya - Exile
Nobody Lives Without Love by Eddie Reader
YouTube - Doctor Who - Rose/Nine - Nobody Lives Without Love
Into the West by Annie Lennox
YouTube - The Return of the King Soundtrack-19-Into the West
No More I Love Yous... (she's wonderfully strange)
YouTube - Annie Lennox - No More "I Love You's"
Milk by Garbage
YouTube - Garbage - Milk
The Trick is to Keep Breathing... (couple second nonsense at the beginning)
YouTube - Garbage - The Trick Is To Keep Breathing [1998 Official Video]
Pleasant dreams are boring...
Further Down the Spiral (The Bottom) by Nine Inch Nails
YouTube - Nine Inch Nails The Downward Spiral (The Bottom)