Invisible Backup Band

It's time for a character to display his incredible musical talent! The stage is set, an audience gathers, he begins to sing and...

Whoa! Where'd this choir come from?

It's the Invisible Backup Band!

When a single character begins to sing or play a musical instrument a capella, he will immediately be accompanied by suitable background instrumentals, vocals or both (and maybe even some neat stage effects) with no conceivable source. Piano, guitar, sax, gospel choir... you name it and it will be a member of the Invisible Backup Band.

Every Musical thrives on this concept.

May or may not accompany Magic Music.

Examples of Invisible Backup Band include:

Anime

Creamy Mami had this effect as part of her Magical Girl powers, which is how she ended up with a career as an idol singer.
In a more literal sense, an episode of A Little Snow Fairy Sugar has the musical accompaniment played by fairies that nobody can see or hear.
The scene in Gundam Wing where Quatre and Trowa play a duet on violin and flute, respectively, while there are also drums and guitar in the background. Apparently a couple of Maganac soldiers were playing right behind the camera.
Azmaria Hendric of Chrono Crusade has a gospel chorus and a soft church organ playing beneath her songs. She also uses Magic Music.
The titular character of Kobato. uses hers in the first episode. She's accompanied not only by a piano, but also by synth effects, a spotlight, and flower petals.
Lampshaded in Ouran High School Host Club: Haruhi is seen singing with beautiful music the background, when someone accidentally unplugs the music player.
Fancy Lala has one in the anime of the same name.
In Macross Frontier, when Ranka begins to sing in public for the first time, initially you can see a guitarist at a music shop add some of his strings to her performance. Hold on, where did all those other instruments come from?!
Lilpri does this whenever they "Himechen" (the shows name for their transformation).

Film

Parodied a bit in Monty Python and the Holy Grail (of course). Any time Herbert even mentions wanting to sing, music starts to play.
Subverted in There's Something About Mary: Every time the theme music was played, a breakaway shot showed two musicians, normally playing from an implausible position.
Used straight in The Girl in Gold Boots with solo guitarist Critter being accompanied by harmonica and other instruments from nowhere. Snarked by the The Mystery Science Theater 3000 guys: "I love the way you play the harmonica with your ass!"
- Ditto for Eegah! "I see he remembered to bring the Isley Brothers camping with him."
- Likewise, in Wild Rebels, when the (anti-)hero is playing guitar for the love interest in the forest, and a horn accompaniment suddenly breaks in:

Crow: Thank you, Brother Squirrel, for the horn!

Road To Zanzibar discusses this together with Mickey Mousing in a Genre Savvy dialogue which ends with Bing Crosby conducting the invisible orchestra to accompany his singing of the love theme:

"What killed me is that from nowhere, an orchestra started. You know, violins and everything, right in the minute of a jungle. Isn't that silly?"

Subverted in Blazing Saddles. Just as you're wondering where the music is coming from, Bart rides past Count Basie and His Orchestra.
Harpo Marx's harp solos are typically accompanied by an invisible orchestra playing quietly in the background. Chico's piano solos are more often unaccompanied, but when he plays "Collegiate" in Horse Feathers the orchestra accompanying him obviously isn't with him in the hotel suite.
The musical pocket watch in For a Few Dollars More is accompanied with what sounds like an orchestra and a mariachi band.
Happens several times in Camp Rock, most noticeably when Shane is singing to Mitchie by the lake. This is very Narmy as the movie is heavily promoted as not being a musical but a "movie with music".
Most of the songs in Tenacious D in The Pick of Destiny have, at the very least, invisible drummers and bass guitarists. A couple also have a guitar playing out of nowhere, or an electric guitar playing when Kage and Jables only have acoustic guitars. "Classico" is probably the only song without an invisible backup band.
A running joke during the making of Star Wars was how come there's sound in space to accompany the fancy special effects shots? George Lucas would claim there was a huge backing orchestra floating around in spacesuits.

Live-Action TV

In the Granada TV adaptation of The Red-Headed League, Sherlock Holmes is accompanied by an imaginary orchestra as he whistles a theme from the concert he attended the previous night.
Once More With Feeling, the Buffy the Vampire Slayer episode. Played straight, lampshaded ("That would explain the huge backing orchestra I couldn't see and the synchronised dancing from the room service chaps"), and even slightly averted. ("She needs backup! Anya, Tara...")
Lampshaded in an episode of Sesame Street with Shari Lewis and Lamb Chop as the episode's guest stars. Shari, Lamb Chop, and Big Bird sing the song "Perfect as a Pig" to Suey the Pig to boost her confidence in being a pig. When the invisible choir echoes the last line of every voice, all four look around for the source and give each other confused looks.
Naturally, this happens a lot in Glee. Sometimes, however, it's averted rather hilariously.
- In one instance, Jesse and Rachel are singing Lionel Richie's "Hello" together. Jesse is shown playing the piano, but string and percussion instruments are heard as well. At first, this appears to be an example of this trope; however, the camera then zooms out to reveal an actual back-up band, materialized out of nowhere.
- In another, Rachel is speaking with her mother, and suggests they sing a song together. After the latter agrees, Rachel calls for her pianist, who again shows up from out of nowhere. Rachel explains "he's always around".
In Twin Peaks, James' song he sings while playing guitar in the episode "Coma" has bass and percussion come out of nowhere halfway through.

Theme Parks

Sonny Eclipse, the animatronic intergalactic lounge lizard at the Magic Kingdom's Cosmic Ray's Starlight Cafe has his Space Angels, who are even the subject of a tribute song that mentions how much he appreciates them even with being unable to see them.

Video Games

This happens quite a bit in Ar tonelico, whenever one of the Reyvateils sings, thanks to their Song Server manifesting the song right as they imagine it, while they sing the main melody.
It pops up in Dragon Age, in a scene at the camp.
This shows up in The Legend of Zelda Spirit Tracks and probably a few of the other games in the series.
Inverted in Loco Roco, everybody is aware of game's background music and sing to it. It's played straight in a few cutscenes.
In No More Heroes, Dr Peace sings a rousing tune when Travis meets him in an empty baseball stadium.

Web Original

Inverted in Dr. Horrible's Sing-Along Blog, where Bad Horse writes letters to scan with his theme tune, and a chorus made up of three of the musical's writers dressed as cowboys lean in from off screen to sing along.

Web Comics

The Arkenhammer of Erfworld functions like this, allowing the attuned user (Stanley) to "Rock Out" by using it like an air-guitar. This confers some massive combat bonuses and is the Titanic aspect of dance fighting. Dance fighting in general seems to use this trope when invoked, but not to nearly the same impressive degree (the Arkenhammer almost deafened Parson when demonstrated in an enclosed space).

Western Animation

Lampshaded in Walt Disney's Mickey, Donald, Goofy: The Three Musketeers, where, after Pete finishes singing his Villain Song, he wonders why the music stopped.
Another lampshade hanging: The Music Meister from Batman the Brave And The Bold had brass and strings for him during one song, synth for another, and crunchy guitar and piano for yet another, even though he had no visible means of producing that music until his big finale, when he was standing in front of a giant stereo system.
And yet another lampshade hanging in Phineas and Ferb The Musical.

We should do it again! This time, as a musical! Whadya say? We'll do all the same things, except we'll break into spontaneous singing and choreography with no discernable music source!