Ojamajo Doremi probably has the most musical references and motifs of any anime series. Even the magical sparks are shaped like musical notes.
When the witches reach a certain lever, their "Poron", or wand, is fused with a musical instrument of their choice. When casting magic, a tune played with said instrument can be heard. In fact, most magical artifacts play short musical tunes in-universe when used, including the transformation taps.
In Dragon Ball GT, the Para Para Brothers used speakers that were built into their body armor that would cause their opponents to dance non-stop, thus leaving them vulnerable to attack.
Violinist of Hameln, a Shōnen parody manga based on the Pied Piper about a guy with a BFS version of a violin who fights demons with magical music. Classical music has never been so badass.
In the Ah! My Goddess manga and movie, particularly powerful and/or complex magical effects can be accomplished through singing (such as the reversal of a spell with both heavenly and demonic components and the recreation of the The World Tree), often but not always in combination with Hermetic Magic.
In RahXephon, both the title mecha and its enemies the Dolems utilize singing as an attack method.
From One Piece, Brook's attacks after the Time Skip count as an example. While the power doesn't come from the music but from the power of his Devil Fruit, he can use his music to "move people's souls" effectively influencing them (e.g., made them believe they are in a party instead of a battle).
Say what you will about Minmay's singing voice, anyone who can sing sixty-foot tall aliens into submission has got something going on.
In Macross II, the Zentraedi have developed their own morale-boost-giving singers, the Marduk Emulators. The plot gets definitely kickstarted when one of them, a girl named Ishtar, is retrieved by Intrepid Reporter Hibiki and starts learning about humanity...
Macross 7 has this as a fundamental part of the premise. The alien antagonists ("Protodeviln") experience literal pain when exposed to music, due to the protagonist's "Anima Spiritia". Sure, it's not genuinely magical, but you wouldn't know that from the laser speaker pods and light show Fire Bomber puts on. (Fire Bomber is one of the best anime acts to ever come out of Japan, and Yoshiki Fukuyama is a rock god. Even dubbed into mediocre English, they rock. Get their albums.)
Sharon Apple, the artificial idol from Macross Plus, took control of the Macross' computer network and sang mankind into a blissful stupor. Granted, she was given the tools to do exactly that by one of her creators... while the other, female lead Myung, is stuck trying to fight her.
In Corrector Yui, Yui and her friends Haruna, Reiko and Akiko were rehearsing a song for their School Festival. it becomes a plot point later, when Yui's I Know You Are In There Somewhere Fight speech to a Brainwashed and Crazy Haruna includes her singing the same song instead of fighting her, breaking through Haruna's brainwashing an reverting her back to who she usually is. Later, Professor Inukai uses Yui's singing as a part of his battle strategy against the Big Bad, who is weak against sone specific sounds, and Haruna returns the favor to Yui by singing the song to her when she's about to lose the battle against Grosser, giving Yui her strength back so she can keep on fighting.
There's a song that causes all listeners to engage in bloody combat, a song that acts as the main character's Theme Music Power-Up, a song that puts everyone to sleep, and a song that causes everyone within earshot to dance uncontrolably.
There was also that incident when both Sun and Lunar were singing at the same time, which caused all humans present (except Nagasumi) to... well, we don't know, because every single person was covered under a wall of Censor buttons.
The manga version of Pretear gives Sasame, the Knight of Sound, the ability to play any musical instrument—and he also seems to be able to soothe people by improvising songs to sing their feelings back to them.
Azmaria Hendrich from Chrono Crusade has the power to heal anyone who hears the song she sings. In the manga, all of the Apostles have the ability to control the Astral Line through music—all of them are shown singing, except for Joshua, who channels his powers by playing an Ominous Pipe Organ instead.
Aria of Tegami Bachi has the ability to heal people's hearts with music played on her violin.
The first two seasons of Onegai My Melody: the magic powers of My Melody and her rival Kuromi are recharged through music, and each season centers around one musical instrument that brings about the end of the world.
When Amiboshi of Fushigi Yuugi takes out his flute, be thankful if he's on your side. If he's not, run.
Mon Colle Knights has Utahime/Kahimi (whose song causes gigantic moving plants to grow) and the Merboy Choir (whose songs cause tidal waves and transformation).
Bolorenof in Hunter × Hunter combines this with Magic Dance: His body has holes in his flesh that, when he dances, vibrates the wind going through them, making him a woodwind instrument. When dancing in certain ways, he produces songs that summon things to attack for him.
In Yu Gi Oh ZEXAL, Yuma uses three Xyz Monsters called Djinns, cute-looking Fiend-Type monsters that use music to fight opposing monsters. (There are actually four of these monsters in the card game, but Yuma has yet to use one of them.)
The Pied Piper, The Flash foe (and later ally) from DC.
Phonogram: Magic is intricately bound up within pop music, and "phonomancers" are magicians who can tap into this for power.
The original Smurfs comic book story The Smurfs and the Magic Flute had the title flute.
The capabilities of Sonic's Mystic Melody in The Blue Blur of Termina range from healing the souls of the lamenting dead to outright time manipulation.
The Wizard in the Shadows takes a cue from Lúthien, and by extension, the Silmarillion. How? Eirian is of half-maia heritage and uses her magic mostly via singing.
The music played by Hurdy of The Tainted Grimoire can cause a variety of effects. Examples include giving a boost to his allies, curing others of status ailments, and do damage to an opponent.
In the Harry Potter fic Hephaestus Harry invented a craft called metaldancing, in which a skilled practitioner could shape metal and give it certain properties by singing while manipulating it with their magic.
Game Theory has magic styles in which the spells are formed with music, and the magitech weapon systems on the Garden of Time are controlled via song.
The Musicians of Ponyville is an Alternate Universe story where the Element Bearers are various musicians (Octavia, Vinyl Scratch, Lyra, Bluenote, Medley and Fluttershy) and the Elements themselves take the form of their preferred instruments, allowing them to defeat the corrupted princesses with a magical concerto.
In Background Pony, Luna's elegies have powerful magic effects such as instilling paranoia or joy, or causing blindness and freezing cold, and they seem to be the only key to unlocking Lyra's curse. Also, the Cosmic Matriarch's song is what created the world in the first place.
This is how the Mane Six summon John to Equestria in the first place, through what is heavily-implied to be the original My Little Pony theme.
As a Bard, this is how most of John's magic works.
Films — Animation
Music repels the Blue Meanie invasion in Yellow Submarine. Especially during All You Need is Love, where the lyrics to the song take physical form as they are being sung.
Pied Piper is one of the best Bounty Hunters in Shrek Forever After. His flute has a dial that can be set to any known creature and makes them dance uncontrollably when he plays. He is first shown riding on the backs of rats into Rumpelstiltskin's palace. He then demonstrates his skill to the witches by making them break-dance. He single-handedly defeats the ogre La Résistance by luring them into a trap and forcing them to dance to "Shake Your Groove Thing". Fiona is not immune, even though she's not a real ogre.
The Harpists from Kung Fu Hustle fight using a guzheng, or Chinese Harp. They can manipulate the vibrations into shapes such razor sharp swords capable of cutting through stone. They are homages to "Six-fingered Fiend of the Zither", a famous villain in old Chinese swordplay films.
Sarah Sanderson sings to get the kids of the town to come to her so she and her sisters can suck the life/youth out of them in Hocus Pocus.
In The Three Stooges short Punch Drunks, Curly is sent into a violent frenzy by "Pop Goes the Weasel".
Masters of the Universe has music with the power of opening up pathways between dimensions. The scientist who first discovered this uses a strange-looking instrument that looks roughly like a miniature high-tech pipe organ with crystals in place of the pipes, but a common keyboard synthesizer works just as well when you know the right notes.
In the Spellsinger series by Alan Dean Foster, the Steve Miller Band's "Fly Like An Eagle" is one of the most powerful magic forces in the universe. It summons the elemental personification of the universe itself, but decreases the lifespan of the universe slightly each time it's used. Generally, the title Spellsingers are mages who work their magic by singing and playing musical instruments. And there is our protagonist, Jon Tom, who is an American student spirited away to this world and who sings rock songs to produce unpredictable results.
The Pied Piper of Hamelin. The Pied Piper used his piping to first lure the rats of Hamelin to their deaths, then later to abduct the children of the town after the people refused to pay him for his services.
Several characters in J. R. R. Tolkien's Middle-earth stories, including The Silmarillion, could achieve magical effects through singing, including Tom Bombadil, Old Man Willow and Lúthien Tinúviel. It helps that Arda, the world of Middle-earth, was literally sung into existence through the Ainulindalë (Music of the Ainur), so anyone with the genealogical and lyrical oomph can do a lot of subtle and overt magic. Finrod the elf sang an illusion into existence, then dueled with Sauron by chanting songs of power. Finrod lost. Lúthien would later also use her music in a duel with Sauron. She won.
And of course Tolkien's inspiration, the sage Väinämöinen of the Finnish national epic The Kalevala. All magic in the Kalevala is done through singing. A natural choice, as the entire epic is done in poetic verse designed to be sung, accompanied with playing of a kantele (a wooden harp).
H.P. Lovecraft used this trope in The Music of Erich Zann. Though strange, bizarre or unearthly music often features in his works, this is the only case of the music itself having power.
In Being a Green Mother (the fifth book in Piers Anthony's Incarnations of Immortality series), the character who becomes Gaea discovers she can control nature with a particular song. (In the next book, another character learns that same song for... other purposes.)
In The Film of the BookThe Lion, the Witch, and the Wardrobe, Mr. Tumnus literally plays Lucy to sleep with a Narnian lullaby (and a really neat flute); the effects are more psychological and ambiguous in the book.
Aslan creates Narnia with a magic song in The Magician's Nephew. This may have been inspired by Middle Earth, as Tolkien and C.S. Lewis were good friends.
L.E. Modesitt, Jr. wrote a series named The Spellsong Cycle in which, if you sing it, it happens, but the energy to make it happen comes from your body. Being accompanied by instruments or other spellsingers helps you do more impressive things without passing out due to exhaustion or starving to death. Most people in that book's universe never learn how to sing, because most wizards don't like having potential rivals around.
In Neil Gaiman's Neverwhere, there is a tune which causes anyone who hears it to give money to the person playing it. Of course, they end up nearly killing the guy, but still... The Magnificent Bastard who taught it did warn that a little went a long way... and picked up a second favor for teaching the street musician the counter ditty.
In Piers Anthony's Apprentice Adept series, it's made explicit that, although Blue's magic can be invoked simply with rhyme, the spells are dramatically stronger if sung (and stronger still if he uses a musical instrument before reciting his chosen spell).
Most of Piers Anthony's books use this trope. His Xanth novels feature triplets named Melody, Harmony and Rhythm, who can "sing and play things real". This can mean anything from turning a girl into a sentient castle to time travel, and they can even identify (though not counter) the magic of the Demons, Xanth's equivalent of gods. Nona, from the Mode series, is fated to overthrow her world's rulers; she can convert others to her cause with a song. Later, she teaches a dragon to stun rats by singing, allowing it to feed on them instead of villagers and completely overhauling a planet's social structure (although Nona didn't come up with the idea). And, as mentioned above, Being a Green Mother in the Incarnations series is magic music incarnate.
Another Piers Anthony book, The Gutbucket Quest, involved a musician transported to a parallel Earth where music and magic were the same thing. The plot involved going on a quest for a magical electric guitar and invoking the loa of Voodoo with the power of Rock and Roll to defeat a corporate demon. (Simple, straight-forward storytelling - gotta love it.)
Rhapsody (the main character of Elizabeth Haydon's Symphony of Ages series) is a Singer, meaning she can use magic channeled through her voice... possibly (the effects of her voice and the definition of "Singer" seem to vary from scene to scene, let alone book to book).
In the Cordwainer Smith short story The Fife of Bodhidharma, the fife can cause either serenity or madness, depending on how it is played.
The necromancers' bells in the Old Kingdom trilogy by Garth Nix can do some dangerous stuff. Different bells give different effects, and the effect also depends on how the bell is played. One of the bells, Astarael, kills everyone who hears it — including the player. More significantly in a setting with functioning necromancy, it sends them "deep into death," killing all but the most powerful victims Deader than Dead so they cannot return, and at least delaying the return of the rest longer than other methods.
The Arthur C. Clarke story The Ultimate Melody revolved around a scientist attempting to reproduce the primal tune from which all music is derived. He succeeded, but on hearing the song, caught it in his head for the rest of his life, rendering him catatonic. On discovering him, his assistant shut off the machine playing the tune, and it was dismantled before it could be reactivated; the assistant was immune to the effect due to being tone-deaf.
One of Robert Rankin's novels features Christeen, sister of Christ (written out of The Bible by the Church), a singer whose voice cures injuries and illness.
War for the Oaks by Emma Bull ends with a duel between the lead singer of a rock band and the Queen of the Unseelie Court for the fate of the city. By this point, the singer's discovered how to use her music to fuel the "glamour" that faeries can use naturally.
The Wayfarer Redemption series by Sara Douglas has magic by music. Its only limitation being that you can't heal anyone unless they're on the brink of death.
The main character in the Bedlam's Bard series by Mercedes Lackey is a Bard, which in that universe means he is possessed of fairly powerful Magic Music.
In Lackey's Bardic Voices series, most of the protagonists have this ability.
In Mike Carey's Felix Castor novels, the main character gets rid of spirits with cantrips played on his tin flute. However, he has to "get the feel" of the ghost first by spending time around it and learning its habits.
In In the Company of Ogres by A. Lee Martinez, the fish-like sirens can use a variety of songs to do things, the main one for seducing people, but there are others, including a song rarely used that can destroy almost anything in its way.
In Tamora Pierce's Protector of the Small quartet, Numair Salmalin uses a flute tune called the Sorcerer's Dance (stated by Word of God to refer to the Sorcerer's Apprentice music) to move boulders for strengthening a wooden palisade. Although the spell is said to be absurdly simple, Numair jacks it up several orders of magnitude by bringing particularly large boulders from ten miles away.
In Lloyd Alexander's Chronicles of Prydain the bard Fflewddur Fflam carries an enchanted harp. His music is not normally magical, but in the last book, The High King, he uses the harp to keep the party from freezing to death. It starts to play by itself when he burns it, giving them the courage to finish the journey. The harp also tends to stretch its strings whenever its owner stretches the truth. As Fflewddur is a born storyteller, many broken strings ensue.
In China Miéville's King Rat, an evil Pied Piper uses music to wrest control of whole classes of animal, by taking control of those animals' totemic leaders. He also uses music to control humans. And that's before he gets the idea of cutting a mix tape, so he can control more than one creature-type at a time....
In Lord Fouls Bane from the Chronicles of Thomas Covenant the Giant Saltheart Foamfollower uses singing to control the boat he is riding down a river. Lord Mhoram also uses a song to summon the Forestal Caerroil Wildwood.
The obscure pulp horror novel Deathsong, by Douglas Borton, is about a Lovecraftian cult that practices music-based black magic. Havoc ensues when they make enemies with a professional singer smart enough to learn songs by ear...
In the Wars of Light and Shadow series by Janny Wurts, bards are capable of some remarkable feats of magic through their music, be it with an instrument or voice alone. Effects range from manipulating emotions, to activating ancient power sources capable of destroying a city, to redirecting surges through those power sources and restoring natural seasonal patterns, to making half an army stand down. According to hints dropped so far, this is the lower end of what's possible.
In Anansi Boys by Neil Gaiman, music was used to create the world, and a sufficiently gifted singer can use songs to cause a Reality Warp. (It helps that the characters in question are the spider-god Anansi and his descendants.)
In the shared universe novel Exiled: Caln of the Claw the Dancers of the Mrem use drums, dance and, in at least one case, bagpipes to strengthen their psychic powers.
The Dresden Files: In Dead Beat, we learn that necromancers require a steady rhythm to maintain control of whatever corpses they've raised. Typically, this can be done by beating a drum, or just tapping a book against your thigh. Or you could use a huge sub-woofer mounted on a car. Necromancy aside, magic can be powered by emotion, and music can inspire emotion; therefore, music is one of many tools available to magic users.
In Shannon Hale's Book of a Thousand Days, Dashti uses this to heal various ailments.
In The Echorium Sequence, the Singers of the titular Echorium use five "Songs of Power" to heal, manipulate, punish, or induce living death.
In Lisa Shearin's "Raine Benares" series, spellsingers are a specialized type of magic user who can channel magic through their voices and cast spells through song. They are particularly effective at influencing emotions.
In Diana Wynne Jones' The Magicians of Caprona this is how most spells work. A particularly amusing example occurs when one of the children decide to use the most powerful song spell ever created, used to drive out an evil devil centuries ago, but with the words changed around to clean the dinner dishes. While it did make the dishes look clean, it backfired when for weeks afterward, anything eaten or cooked with those dishes wound up having a greasy, soapy taste. Oops.
Also, the nix is a harpist and lures Jenny with it.
Terry Brooks's world of Shannara has the wishsong, in which several protagonists, all elven descendents, can create potent melodies of creation and destruction.
In Wody Głębokie Jak Niebo some mages write their demon binding spells in the form of songs to make it harder for others to steal their work. Sirocco can control demons through her singing without binding them permanently.
A sketch from British TV comedy series That Mitchell and Webb Look had a man being given a green clarinet which, when played at someone, caused them to dance and sing an embarrassing truth about themselves. He used it to live a life of luxury, until another person was given a red tuba which caused... well, an unfortunate comeuppance.
In an old The Kids in the Hall sketch, Satan is driven back into Hell by the "Holy Trinity" of guitar chords (E-A-B, or the opening chords of Smoke on the Water).
The Outer Limits: In "Music of the Spheres", the titular music is a signal from space which, in addition to being extremely addictive, ends up causing a series of dramatic physical transformations in listeners. Notably, unlike most Brown Notes, the changes the music causes ultimately turn out to be beneficial.
A couple Monsters Of The Week used music too, such as the Gnarly Gnome and Guitardo. (There was an ironic twist with the first one; he used his music to hypnotize some teenagers, hoping to lure the Rangers into an ambush, but the plan had a Fatal Flaw that he didn't count on: one member of the group he targeted was hearing impared, managed to escape, and warn them, ruining any chance of a surpise attack.)
In the premiere of the BBC series Merlin a witch, magically disguised as a famous singer sings a song that causes the entire court of Camelot to fall into an enchanted slumber so she can assassinate Arthur. Luckily Merlin instinctively recognises the magic and covers his ears in time.
Most seasons only use music as incidental sound effects during transformations or special attacks, but Kamen Rider Kiva has a violin-playing protagonist, and one episode had him playing the mystically-created violin built by his father to force himself into shapeshifting. His sentient Transformation Trinket, Kivat, uses whistles to summon weapons, call Castle Doran, or even start Kiva's Rider Kick.
Then there's Kamen Rider Hibiki, where the enemies can only be fought using "pure sound". The Transformation Trinkets are weaponized instruments, as well, and each Rider carries a set of Disc Animals, which when not in use fold up into compact discs.
Buffy the Vampire Slayer, with the episode "Once More with Feeling". A musical demon causes life in the entire town to be a musical. Doesn't seem too bad, until it's revealed you uncontrollably spill your deepest secrets in songs sooner or later. And sooner or later, you will dance and sing yourself into a fiery death (the demon is stopped before more than a handful of Sunnydalians burn). Relatedly, the demon claims to have given the inattentive Roman emperor "his very first fiddle", thus also dovetailing with the trope.
Angel has a bit of a variation: Lorne's singing abilities (great though they are) don't confer any magical effects, but when he hears other people sing, than he is able to read their destinies. Well, he is able to sing high enough to cause physical pain to people and incapacitate them. And even ordinary singing is too much for most inhabitants of his dimension.
Used in Warehouse 13 when a group of bank robbers commit crimes by playing a specific song that sends the listener into blissed-out ecstasy, then taking the money while they're incapacitated.
Emma from Heroes has this power; so far we've seen her use her cello to summon people she is thinking about and make a crack in her apartment wall.
"The Lyre of Orpheus" by Nick Cave and the Bad Seeds
Look what I've made, cried Orpheus
And he plucked a gentle note
Eurydice's eyes popped from their sockets
And her tongue burst through her throat
Myths & Religion
Not just The Kalevala, traditional Finnish magic in general consisted of spellsongs that were either sung or chanted, depending on the context. This makes sense, because most spells were essentially short stories relating the mythological origin of things like fire, iron, living things and such, because knowing the primordial nature of a thing was thought to give power over it. As such, spells were passed down by teaching them as songs, often as part of larger epics or stories, with the poetic meter ensuring the fidelity of the oral transmission. Notably, sages also apparently engaged in contests of magical knowledge which were conducted by singing as many spells as they could remember; many thousands were recorded in the 19th and early 20th century.
Similarly, the Ancient Greeks actually believed music was magical. They had a single word that meant both "to sing a song" and "to cast a spell." This is most obvious in the story of Orpheus, mentioned above. It also shows up in the teachings of Greek philosophers - Plato's writings appear to be in a 12-note chromatic scale, and most famously Pythagoras first realized he could predict things using math (physics, basically) by observing the strings of his lyre, and went on to incorporate divine music into his belief system.
This has carried over to Italian language: the verb "cantare" both means "to sing a song" and "to cast a spell".
Orpheus, who sang so well he (almost) restored his wife to life. And made the Furies weep. And made trees pick up their roots and rocks roll over to him just so they could listen.
Orpheus, with his lute, made trees and the mountain tops that freeze, Bow themselves when he did sing: To his music, plants and flowers Ever sprung; as sun and showers There had made a lasting spring. Ev’ry thing that heard him play, E’vn the billows of the sea, Hung their heads and then lay by...
No matter what the medium, mermaids are almost universally given magic singing voices:
The unearthly singing of the sirens in Homer's The Odyssey. These weren't originally mermaids (they're supposed to be part-bird), but over the years, their association with the sea (and the Latin word for mermaid, sirena) made them into mermaids.
The trumpets that when blown made the walls of Jericho fall down, in The Bible. Had nothing to do with the fact they were trumpets; it was a case of faithful obedience. In theory, the Lord could have told them to do the Hokey Pokey, and the walls would have still fallen if they'd done so just as He told them to.
The Irish legend of the harp of Daghda, which could cause pain, laughter, or peace through music.
The Irish filidh could also do that. Accordingly they were held on the same level as the kings of Ireland, since they could destroy their reputation (and potentially maim them) with a song.
In the Swedish legend of the Hĺrgadance a mysterious fiddler turned up one day in the village of Hĺrga during a celebration and started playing a song on his violin that made everyone dance enthusiastically. Too late, the people realized that the man, who they now saw had a goat's leg, was the Devil himself. They were unable to stop dancing, and kept doing so while the fiddler led them up the nearby Hĺrgamountain. There, he kept playing until everyone had been killed and their bodies torn to bits by the intense dancing. The top of Hĺrgamountain is still flat to this day because of the wild dance.
In 3rd Edition D&D, Bards can not only play magical music, but can also cast spells — but unlike any other class, every spell they cast has a vocal component, and also unlike any other class, they cannot cast silent spells as a bard even if they would have the ability to do so otherwise.
The 2nd Edition sourcebookPlayer's Option: Spells and Magic introduces the Song Mage, who faces the same restrictions.
Supplemental 3rd Edition material results in new ways to "spend" bardic songs, alternate bardic music to learn, ways to further combine music and magic, prestige classes like the Virtuoso and Lyric Thaumaturge, new instrument types, and bayonets to suit lutes, flutes, and fiddles of every size.
The 3rd Ed Dungeon Master's Guide features a number of magical music instruments, such as bells, lyres, drums, flutes, and pipes that have helpful or harmful effects. Satyrs' pipes are especially fun.
Don't forget all those monsters with hypnotic songs, like harpies or cloakers.
In In Nomine reality is controlled by something called "the Symphony;" the setting's "magic" consists of manipulating the Symphony in a couple of different ways. The most direct, used by angels and demons (and some special humans) are Songs, which are basically specific melodies which (when coupled with Essence expenditure) produce all sorts of special effects from healing to blowing stuff up. The less experienced have to actually vocalize the Song (and perform specific movements/gestures), while the more skilled can just invoke them mentally. The use of Songs creates "disturbances" in the Symphony which can be tracked down to their source (both the place and the person) by anyone with supernatural abilities who is close enough and perceptive enough to "hear" them.
In Shadowrun/Earthdawn, Thayla's singing was so beautiful it could keep the Horrors at bay.
In Ars Magica the Enchanting Music ability fits the mold as do the "Holy Music" (Holy) Method and the magic of the Hyperborean Hymnists. Certain applications of Performance Magic and the Enchantment (Faerie) Method also work.
Pavane of Slaanesh ability (and its big brother, the Grand Pavane) of Chaos Daemons in Warhammer 40,000 is described as magic music that forces those who hear it start dancing and fall under the daemon's control.
Many, many witches, wizards, sorcerers, and sorceresses sing incantations.
Tamino's flute and Papageno's glockenspiel in Mozart's The Magic Flute. The Queen of the Night casts spells, arguably, with her dazzling coloratura passages.
In Wicked, Elphaba sings "Eleka Namen Atum Atum Eleka Namen; Eleka Namen Atum Atum Eleka Namen," and then proceeds to lampshade this with "What good is this chanting? I don't even know what I'm reading!"
MMORPGs tend to be hungry for new classes, and often feature a bard class who uses this.
Most spells in The Legend of Zelda series require Link to use an instrument and a certain tune to cast them. This tradition was started in the original game. It had a flute with certain magical effects.
Very Prominently used in Ocarina of Time (of course), Majora's Mask, and The Wind Waker, with several varieties of magical effects available through music, but nearly every game has at least one example of Magic Music, most often as the Warp Whistle.
Taken to the fullest extent of the trope in Link's Awakening, where the 8 Instruments of the Sirens were required to wake the Wind Fish and leave the island, in addition to having an ocarina which had 3 plotdevice songs.
It was obvious that Spirit Tracks would go with this Trope ever since it was revealed that the game's Japanese name was "Earth`s Whistle". The "whistle" was revealed to be the Pan-flute like "Spirit Pipes", which are played by using the touchscreen and microphone in tandem. They work almost identically to magic instruments from earlier games. You also play duets with the Lokomo and Zelda with instruments such as bass, shamisen, flute, drums, and oboe, and to some extent... a pair of vocal cords. Which are held by Gage, Steem, Carben, Embrose, Rael and Zelda respectively.
Skyward Sword has the harp, which is stated from the very beginning to have been passed down by the goddess. Fi also dances along to the songs that Link plays. Oracle of Ages also has a harp, which is used to travel through time.
Elena in Grandia II sings a song that seemingly lifts the spirits of everyone in the world, brings Ryudo back from oblivion, and gives the heroes the power to defeat a dark god.
Pokémon just loves to abuse this trope. The Pokéflute/Pokémon Whistle can magically wake Pokémon up. In Pokémon Gold and Silver, in lieu of a Pokéflute, you can tune to a certain radio station to wake your Pokémon up. Another radio station, depending on the time of day, an increase or decrease encounter rates with the Pokémon March and Pokémon Lullaby respectively. In Diamond and Pearl, the event item Azure Flute is used to awaken Arceus. In fact, a good number of the sound-based moves in the game are musical.
Mystearica "Tear" Grants uses this in six of her spells, the pieces of Yulia's Grand Fonic Hymn. It in and of itself is not used in combat, nor is the Seventh Hymn. They do provide Cutscene Power in the fight with Van though.
Some magic is sound based in this game, namely the Seventh Fonon, the Fonon of Sound. Unlike the six other Fonons which are based on your typical Elemental Magic, the Seventh Fonon was created as a mutation of the other six in the Planet Storm. The Seventh Fonon can be used for reading the Score, Daathic Artes, and, you guessed it, Fonic Hymns.
An ocarina and its music were also the source of your power in the Jade Cocoon games.
In La-Mulana, an ocarina is required to speak with the Sages.
Edward in Final Fantasy IV can inflict damage on enemies, as well as confuse them and put them to sleep, with his harp-playing. He can't be considered a terrible musician; just one that knows his audience, given in the DS remake he can learn Life's Anthem, which rapidly restores the HP of the party as long as he isn't interrupted. And then there's the songs available to the Bardsong Augment...
Speaking of Edward, another song used in the game, though not in combat, is one he learned to dispel evil spirits. Coupled with Whisperweed, this is how he cripples the Dark Elf's magnetic powers.
Edwards revamped abilities are likely inspired by the Bard class of Final Fantasy V, which could use several useful songs, for instance to speed up the other party members, restoring mana over time or dealing heavy damage to undead enemies.
The Bard class has existed for a while in Final Fantasy, including Final Fantasy III and Final Fantasy Tactics; in fact, Hurdy's ability list, other than Hide, is taken practically verbatim from Final Fantasy Tactics.
Final Fantasy X-2 has the Songstress class, which is a pop star combination of the standard bard and dancer. It combines magic music to buff the party and magical dances to screw with the enemy.
The all-female race of Reyvateils was created with the ability to create various magical effects through their songs. This includes things like healing, creating elemental bursts, summoning beings to attack, or even (on the upper scale of things) creating entire continents.
"Magical languages" (Hymmnos, Pastalia, Risshizentsukyomi and Ar Ciela) are used to create the really earth-shattering effects.
Note that the entire game world depends on song magic. Airships run on symphonic power, item crafting is due to applied "Wave Theory" (yes, fictional physics), the initial singularity sung the universe...
In Kingdom Hearts, Demyx (the Melodious Nocturne of Organization XIII) uses a blue sitar that's bigger than he is to summon water-clones. It also makes for a really effective club.
There is also the Symphony Master from "Kingdom Hearts:Birth by Sleep" , that attacks by summoning a trumpet, a drum, and a violin and near blows Terra to Kingdom Come before the fight.
The Eight Melodies (Queen Mary's Song) from Mother/Earthbound Zero, is an interesting example of this trope. While you learn each melody from some really interesting places (including a singing cactus), the song itself is not magical. The real power of the song comes from the memories associated with it, which is why it only has an effect on Queen Mary and Gigyas.
This trope is the central mechanic of Rhapsody A Musical Adventure. The heroine Cornet controls her puppet army by playing her magical trumpet.
The girl in Tombs And Treasure for the NES could create various magical effects, primarily directing the sun's rays and turning flesh to stone, by playing a set of golden panpipes.
Legend of Mana lets you cast spells using magical instruments. Each instrument has its own spell, and you gain stronger ones through Item Crafting using elemental coins and a variety of materials.
In Infinite Undiscovery, Capell obtains a flute from a claridian named Saruleus, which allows him to play music that can dispel illusions among other effects. It's just a pity that the one song that really counts, the one that stops them from hitting the Lunar induced Berserk Button, turns out to be pretty ineffective unless played constantly, which is impractical.
Ricardo from Shadow Hearts: From the New World can play songs with his guitar for various effects, from casting positive status effects on the party, sans himself. More songs can be composed when Ricardo find new items as his inspiration.
Aquaria. The protagonist Naija sings songs to change her form or to cast a spell, while a nine-note motif, foreshadowed in the soundtrack, turns out to be an important part of The Reveal.
A mermaid song (see myth and legend above) is used to rid a town of monsters in Chrono Cross. And then of course, there's the song that defeats the final boss and gets you the Golden Ending.
In Mabinogi, ranking musical skills high enough gives characters the ability to play music that can buff teammates, debuff mobs, and even mind-control single enemies.
It is said that Mystia's singing can cause night-blindness.
Not to mention the Prismriver Sisters, a trio of musical poltergeists who use their instruments for Bullet Hell. Each sister's music is also said to have an emotional impact on the listener: Merlin's makes you peppy, Lunasa's makes you depressed, and Lyrica's deadens your feelings altogether.
There is a story arc in City of Heroes that involves recovering "The Dirge of Chaos" before it can be broadcast over Paragon City's airwaves.
In Kingdom of Loathing, the Accordion Thief can play various songs that will provide buffs to themselves or other players - for example, "Ode to Booze" increases the adventures you get from drinking alcoholic beverages, "Fat Leon's Phat Loot Lyric" boosts item drops, and "Polka of Plenty" increases Meat drops.
Ys I: One purple area of Darm Tower has creepy music that hurts you until you smash the pillar where it is coming from.
The Hunting Horn weapon in the Monster Hunter series can bestow its player and their allies with a huge variety of different beneficial effects that emulate those of various items and equipment skills, such as healing, status ailment removal, and immunity to monster roars. Each horn has a limited selection of songs it can play for the sake of keeping it balanced, though.
The Qurupeco is able to produce similar benefits for itself and other monsters in its vicinity by singing. However, hitting its throat sac before it finishes a song can cause it to mess up and heal/buff you, instead.
Most of the combat system in Double Dragon Neon revolves around collecting mixtapes to gain statboosts and new abilities and attacks, and using the Tapesmith to make them stronger via mythril.
Mario and Luigi Dream Team has the Dreambeats, which cause any ordinary person who hears them to immediately fall asleep. Antasma and Bowser use their power to knock out the population of Pi'illo Isle and use their dream energy to power the Dream Stone.
The Mariachi Guys in Paper Mario: Sticker Star are able to provide enemies with a variety of stat boosts using their guitar tunes. While they never attempt to engage Mario in combat on their own, they'll Flash Step over to him and join in on any battles that are started within earshot of their music. Made more annoying by the fact that they'll run away if they're the only enemy left in battle, plus they're usually hiding in the field, which can make getting rid of them for good rather difficult.
The Secret World: A few places in the game. The siren song near the beginning is produced by some artifact that keeps the fog away. Later, in egypt, the singing of the sentinels keeps a great evil sealed away, later still, you find out that the gaia engines, that you encounter towards the end of the New England and Transylvania main stories, act as music boxes to keep the dreamers asleep.
Joelle from  uses music-based skills, which affects the entire party. Her songs can heal and buff up allies, while debuffs, or put status effects on, enemies.
This is Jimmy's speciality in South Park: The Stick of Truth. It replenishes power-points, applies buffs and debuffs, puts enemies to sleep, and makes them shit blood.
One of the trademarks of the Heterodyne family in Girl Genius is their way of "Heterodyning", or humming in a very complicated way which helps the Spark at work to concentrate. While not music that causes magic by itself, certainly a side effect and assistant to the Sparkiness.
Soul Symphony: In the Soul World, music can be used as magical spells. Olivia, a musical prodigy, gains flight and barrier powers from playing scales and trills on her clarinet.
In The Challenges of Zona, Mentl, a second-rate busker from our world finds himself, like Jon-Tom in the Spellsinger series, transported to a magical world where he finds that his skill at and knowledge of modern music has devastating effects both on the ladies and on his enemies.
The Smurfs love magical music. One episode has Harmony Smurf playing a magical bagpipe that put all the other Smurfs into comas. Indeed, the original Smurfs movie, The Smurfs and the Magic Flute, was about them cutting down a huge tree to carve a tiny little magic flute... and that's for stopping somebody who has another magic flute that they made.
Roberon in Robotman and Friends uses a magical flute. He uses it to activate his power using an eerie, atonal six-note little tune (which some compare to the Spider-Man theme song!). This is despite fact Roberon hates music because it causes him physical agony and he needs to have his sidekick Sound-Off cover his ears for him. Or, well, whatever a robot has which passes for ears. So he's a music-hating villain with music-based powers!
Music can have a profound, if temporary, effect on neural performance. This is frequently referred to as the Mozart Effect, and possibly qualifies as a real-life version of a buff or debuff. Alternatively, sound of the wrong kind can increase stress and even cause health issues (see Brown Note).
Shortly after the folk song Fhear a bhata had been composed, the mentioned boatman came back and married the composer.
If you're willing to stretch the definition of "music," there's acoustic levitation, by which a loud sound can be used to lift a small object.