Ethereal Choir

A distant choir singing in harmony to accompany a scene, often a capella. This is not rhythmic like Ominous Latin Chanting; usually you won't hear any words because they're only singing vowel tones. The effect is general otherworldliness, and the tone can range from consoling to chilling.

This is related to the One-Woman Wail, which it sometimes accompanies. See also: Creepy Children Singing, where creepy songs and nursery rhymes are played in the background to add tension and fear to a scene.

Examples of Ethereal Choir include:

Anime and Manga

One of the main themes of Ghost in the Shell is a slightly dischordant choir singing a capella.
Bleach uses this with a weird electronic effect in a lot of scenes.

Film

The approach to Cloud City in Star Wars: The Empire Strikes Back.
An absolutely epic one when the ents march to trash Isengard in the Two Towers from Peter Jackson's Lord of the Rings.
- A part of the theme "Nature's Reclamation" used several times over the course of the movies, and is essentially this. It sounds when Theoden resolves to ride out against the Uruk Hai at Helm's Deep, and again in Return of the King when the Eagles dive out of the sky to attack the Nazgul.
Parodied during Ted and Elaine's big kiss scene at the end of Airplane!, where the choir goes horribly out of tune .
Used fairly heavily in Coraline's soundtrack, to great atmospheric effect.
An ethereal little melody is featured repeatedly on The Prince of Egypt soundtrack to great effect.
The Ark theme from Raiders of the Lost Ark.
In 1951's A Christmas Carol, Scrooge hears the wailing of Marley's fellow doomed spirits at the end of the latter's visit, and again later when taken to his own grave.
In Kingdom of Heaven, after Baldwin dies, a choir starts singing as Jerusalem mourns.
In 2001: A Space Odyssey, G. Ligeti's 'Requiem' is used with the apelike proto-humans (and later the less ape-like humans) encountering the uncomprehensible.
In The Presidents Analyst, the title character starts to crack up - he sees men in black suits and sunglasses ostensibly out to get him everywhere, punctuated with an alarming piece of vocalese.
The 2009 Star Trek film employs one, singing a variation of the main theme amidst the dramatic silence of space when the Narada is finally being broken up and consumed by the combination of a black hole and the weapons of the Enterprise.
Titanic used heavily synthesized vocals to make a chorus during the sinking.

Live-Action TV

One of the pieces of stock background music in Monty Python and the Holy Grail.
Used at various points throughout the Murray Gold scores for Doctor Who. Generally acting as a musical personification of Time, although this sometimes ends up as a One-Woman Wail. For the Daleks it becomes Ominous Latin Chanting. Notable at the end of "Gridlock", when the population of New Earth sings an acapella version of Abide with Me.
On Glee, the beginning or end of a scene or something dramatic happening is accompanied by a "doo ba doo ba doo ba doo" or "doooo-BOP"
Part of the theme song in Power Rangers Zeo.

Music

A staple of Danny Elfman's work.
Holst's Planets ends with an Ethereal Choir whose voices slowly fade away after the orchestra stops playing.
The opening verse to The Rolling Stones' "You Can't Always Get What You Want" is sang like this.
Frequently featured in Nox Arcana's work.
Immediate Music's Requiem Rave fuses fast electronic beats with a mostly female choir singing vowel tones.
"Lady in Black" by Bad Boys Blue uses this.
"Welcome to my Realm" by Fireaxe is sung by the devil, and uses an ethereal choir provided by the screams of the damned.

Tabletop Games

Warhammer 40,000 has the choir of the astronomican that psykers and the occasional pious Space Marine can hear.

Theatre

Used for surreal effect in the overture to Willy Russell's stage musical Blood Brothers.
Ravel's Daphnis and Chloe has its wordless chorus sing unaccompanied during a blackout between scenes.
The scene in the musical Brigadoon where Mr. Lundie talks about hearing voices from the outside world.

Video Games

Zora's Domain in The Legend of Zelda Ocarina of Time. The Forest Temple and Stone Tower have ominous ethereal choir.
Metroid Prime 3: Corruption has this in their main theme.
The song "High Charity" in Halo 2. Also used in the Halo 2 version of the title theme, and "Heroes Also Fall" and "Roll Call" in Halo 3.
Baten Kaitos uses this music as in the Interdimensional Cracks. It's not ominous enough for Ominous Latin Chanting - though it borders on it. It's more there just to add drama to the idea that you're entering a different dimension.
- Choirs are also used in other songs, mostly late-game songs. Sometimes used in conjunction with One-Woman Wail if something really bad's going on.
The Enchantress Y'gael is rather annoyed at the Ethereal Choir repeating whatever she says in a sing-song tone when you encounter her in Zork: Grand Inquisitor.
Used starkly near the end of Xenogears.
The music used in the main menu of Ninety-Nine Nights (N3) counts, and also doubles as One-Woman Wail.
Along with Ominous Latin Chanting and One-Woman Wail, Nier's soundtrack tends to use a lot of this (e.g. Snow in Summer).
The Cherubic Choir of Shin Megami Tensei: Strange Journey's "Theme Of Law" was designed for the "chilling" effect, especially given the intentions of the Three Angels and Mastema for you and Zelenin.
"Velvet Room," aka "The Poem/Aria for Everyone's Souls" in the Persona series (and augmented as "The Battle For Everyone's Souls" in Persona 3), is exactly this, to enhance the otherwordly, mystical atmosphere of the Velvet Room. In the first two (three if you count both Persona 2s) games it was explicitly sung by Igor's assistant, Belladonna, but by the time of Persona 3 and 4 there was no place for the opera diva anymore.
- It also gets a face-melting rocked-out version in Persona 3 as "The Battle For Everyone's Souls", with the One-Woman Wail intact.
The music "Amongst The Dead" in Medal of Honor: Underground has an ominous version of this.
The Judge, the final boss theme from Kamui, uses this.
Guilty Gear and BlazBlue use this along with One-Woman Wails and Ominous Latin Chanting mainly for final boss themes like "Meet Again" and "Awakening the Chaos".
Some themes in Koumajou Densetsu also use this.
Rosenkreuzstilette uses Ethereal Choirs and Ominous Latin Chanting in songs like "Heavenly Snow Dance ~Entirely Pure~", the opening scene theme, "Dark Purple Moonlight", Grolla's stage theme, and "Last Battle ~Requiem for Myself~", the final boss theme.
White light from Okami.
Baldur's Gate: Dark Alliance has this during the absolutely epic Final Boss music, in a perfect balance between grandly chilling (verges on Ominous Latin Chanting but without the lyrics) and heart-breaking (entirely appropriate, considering the final boss is a Well-Intentioned Extremist Anti-Villain bordering on Woobie, Destroyer of Worlds): Last Battle - Eldrith the Betrayer (0:47 to 1:03 for the first iteration).
Just about all the .hack games.
In Dark Souls, if the music isn't If it isn't Ominous Latin Chanting or a One-Woman Wail, it's this. Often times Ominous Latin Chanting and Ethereal Choir are both present.

Web Comics

Ursula Vernon's Digger marks the appearance of ghosts with the sound of an ethereal choir. Because, as the author points out, "there is no feasible onomatopoeia for this," the sound is represented by the Unsound Effect of "sounds of distant ethereal chanting!" and variants.

Web Original

Broken Saints features this in a number of pieces. Some of the pieces are original music, some are classical works, some alternate with Ominous Latin Chanting, and one of them does include a One-Woman Wail.

Western Animation

Parodied in a later episode of Johnny Bravo. The choir accompanies the appearance of a large ad that happens to be about the very thing Johnny needed the most in that particular scene. The camera then pans to slightly, revealing an actual church choir.
"Inner Sanctum/The Nesting Grounds" from Disney's Dinosaur.