Futuristic Theremin Wail

"No instrument says "You're in outer space!" more than a small cigar box with a radio aerial stuck to it."

—Mark Kermode

"It hasn't got six strings, but it's a lot of fun!"

—Jimmy Page

The theremin (aka termenvox) is an electronic instrument developed in the 1920s. The player waves his hands near its antennas, using the electrical conductance of the body to alter the sound. It creates a very pure tone, and sounds like a lower-pitched version of someone tuning in an old-fashioned radio to a test signal. It's essentially a primitive analog synthesizer with an Unusual User Interface, or a Real Life Xenophone.

The retrofuturistic and haunting sound of the Theremin is closely associated with Speculative Fiction and horror from the black-and-white era, but it shows up in some very odd places.

Examples of Futuristic Theremin Wail include:

Anime and Manga

In Nodame Cantabile, there is an extremely creepy girl who resembles and is mistaken for by some to be a Stringy-Haired Ghost Girl, whose favorite instrument to play is the theremin.
In Chapter 2 of Saint Young Men, the music-related sidenote about Jesus says that "he's curious about theremins".

Film

First used in a Hollywood score in Hitchcocks's Spellbound
The Lost Weekend, about a alcoholic's weekend-long binge.
The Day the Earth Stood Still is one of its most famous uses.
Used in Tim Burton's bio-pic Ed Wood, to recreate the theme music from Plan 9 from Outer Space.
Used to represent altered reality in eXistenZ and The Machinist.
And in countless Horror and Science Fiction B-movies between 1945 and 1960. In those times, if it wailed, it was usually a theremin.
The Delicate Delinquent, a Jerry Lewis film from the late fifties, was unusual for having an actual theremin on screen instead of just using it for the score. It's mined for physical comedy, as Lewis' character stumbles upon it, slowly figures out that it's sounds are corresponding to his movements, and starts dancing around it.

Live Action TV

The opening to Doctor Who doesn't use one, but evokes the sound. The musicians in this case actually cobbled some parts from the technical department and built a synthesizer to simulate it.
The melody of the theme of Star Trek: The Original Series was actually never played on a theremin. A soprano singer emulated its signature sound.
The Midsomer Murders theme and underscore uses it, to great, creepy effect.
The theme music to Dark Shadows does, as well.
Sheldon Cooper from The Big Bang Theory plays the theremin. Badly.
Harry Lubin, composer for One Step Beyond and the second season of The Outer Limits (TOS), used the theremin extensively in his sscores for both series.

Music

The Beach Boys' "Good Vibrations" features a Tannerin (aka an Electro-Theremin, basically a theremin with mechanical controls for pitch and volume) in the chorus.
"Whole Lotta Love" by Led Zeppelin.
The '60s psychedelic band Lothar and the Hand People was known for using the theremin.
The punk-reggae band The Dingees featured a guest thereminist on two tracks from The Crucial Conspiracy, "Summertime" and "We Rot the Voodoo". It fit well with the album's sci-fi Conspiracy Theorist themes.
Converge used this extensively on their Jane Doe album, to genuinely heart-stopping effect.
"Velouria" by the Pixies.
The Hungarian space rock band Omega has always loved the theremin, and it shows up in multiple songs.
The Road Hammers may be the only country music band in history to use one.
Vadim from Dragon Force (video game) plays one in addition to keyboard.
John Otway uses a theremin in part of his cover of Crazy Horses. He doesn't so much play it, as use it to replace the screams in the refrain.
Bill Bailey uses it as part of his keyboard setup, usually for comedic effect.
Several of Doctor Steel's songs encorporate the theremin (or at least samples of theremins).
Possibly subverted in the B-52's song "Planet Claire"—it sounds like they use a theremin at one point, but that's actually Kate Pierson's voice.
In their more recent live shows, Simon and Garfunkel have used a theremin player for the instrumental break in "The Boxer".
"Mysterons" by Portishead.
Used in Stab My Back by the All-American Rejects.
Covenant's first hit single was named "Theremin", but it does not use the instrument of the same name.
Notably used on "Electricity" and "Autumn's Child", both by Captain Beefheart.
Japanese electropop artist Aira Mitsuki released a single called "Aira no Kagaku CD" (translated as Aira's Science CD). There are two tracks that prominently feature the Theremin - a song called Science Music and her cover of Merry Christmas Mr Lawrence called Senjou no Merry Christmas.
20th-century composer Percy Grainger wrote for an ensemble of four to six Theremins (instead of a string quartet) in his composition "Free Music," utilizing their potential for notes of indeterminate pitch.
The Other Wiki lists several composers of 20th-century concert music who called for Theremins in their instrumentation: Bohuslav Martinů, Percy Grainger, Christian Wolff, Joseph Schillinger, Moritz Eggert, Iraida Yusupova, Jorge Antunes, Vladimir Komarov and Anis Fuleihan.
Used rather poignantly on Ulver's Shadows of the Sun album.
Ska/punk/funk band Fishbone makes use of a theremin.

Video Games

Destroy All Humans! uses it to evoke the 1950s alien invasion films which it parodies.
The Movies uses a theremin sound as the stock sound effect for handling a Sci Fi script.
Vampire Bloodlines has a theremin playing all the way through Dr. Grout's (a batshit insane leader of an equally insane vampiric clan) mansion.
In episode 3 of Strong Bad's Cool Game For Attractive People, Homsar plays the theremin in Strong Bad's band D-Ö-I. A giant theremin, that he plays by levitating and moving his whole body up and down
Sonic the Hedgehog 2's final zone has a very long, theremin-heavy theme tune, the last vestige of a Dummied Out level.
- The Egg Carrier theme in Sonic Adventure also uses it, starting at 0:45.
Liberally used in the soundtrack for Banjo-Kazooie and its sequels. The levels where it shows up are meant to evoke the feeling of a classic horror B-Movie, Atlantis and an alien terrarium.
A pocket theremin is a usable weapon in Kingdom of Loathing.
Descent 3 uses a theremin-style synth for its main theme, as well as for the pentatonic Asian riff heard in Level 4.
Welcome to the Machine from Ecco the Dolphin.
Ray Storm uses it in the infamously nightmarish "Molecular Clock" boss music.

Web Original

A theremin makes a last-minute appearance in the ending sequence of Dr. Horrible's Sing-Along Blog, re-doing the opening theme.

Web Comics

In the various musical tracks that accompany Homestuck, Jack Noir is often leitmotifed by what sounds like a theremin.

Western Animation

I.R. Baboon plays a Theremin in one episode of I Am Weasel, which somehow keeps causing earthquakes.
In an episode of The Simpsons, they hear what they think is a ghost haunting their attic. On their way up to investigate, the obligatory spooky theremin music starts playing. Homer hears the music and is not happy about the ghost getting ahold of his theremin.
- Despite being often featured on the soundtrack, it wasn't until the 2011 Treehouse of Horror episode that an actual theremin was used. (Before that, it was emulated by a synthesizer)
Used in an episode of American Dad. While flashing back to the day he met Roger at Area 51, the theremin plays in the background. Stan could apparently hear it as he stops and says he's going to check the room its coming from.
In a post-revival episode of Futurama, Bender dies and takes on a ghostly existence. When the characters call a séance to exorcise the ghost, cue the creepy Theremin track, but when the Establishing Shot ends, it is Zoidberg playing it to his coleagues.