Magical Flutist

This character is notable for having a flute or some other wind instrument, playing tunes that give a feeling of mystery or magic, and for being quite mysterious themselves. Bonus points if this character is a representation of nature or has the power of mind control or summoning.

Examples of Magical Flutist include:

Anime and Manga

A Little Snow Fairy Sugar -- The title character, using her flute to create snow.
Fushigi Yuugi -- Amiboshi
Naruto -- Tayuya is this and Musical Assassin. She can manipulate demonic dolls using it, as well as casting illusions.
From Magi Labyrinth of Magic, this is how Aladdin summons Uugo, and how Pisti can befriend animals.

Comic Books

The Smurfs and the Magic Flute and its 2008 prequel The Flute Smurfers. See also Western Animation.

Fairy Tales

The Pied Piper of Hamelin -- The titular character is this.

Film

Clash of the Titans remake—Subverted: The soldiers with Perseus have made camp, and one of them pulls a flute out of a bag. This film being what it is, you expect it to do something magical. He starts playing... and he's terrible, and nothing special happens. The lead soldier asks to see it, breaks it in half, and throws it aside. The player just gives him a level look, pulls another flute out of the bag and starts playing it just as poorly as before.
The Dark Crystal - Jen's split flute comes in handy for identifying the true shard and in a bonding scene with fellow Gelfling Kira.
Escape to Witch Mountain (1975) -- Tony plays a harmonica to increase his telekinetic powers.
Kill Bill - Bill plays a wooden flute which lends to his mysteriousness.
Live and Let Die—One of James Bond's opponents is a man who plays the role of the voodoo loa Baron Samedi. Bond once encounters him while he's playing a flute. After apparently being killed by venomous snakes, at the end he appears riding the front of a train, indicating that he may be the real Baron Samedi.
Willy Wonka and The Chocolate Factory—Wonka uses a flute to issue commands to the Oompa-Loompas.

Literature

Edgar Pangborn—His short story "Tiger Boy" might count. The eponymous youth plays a set of pan pipes, runs wild and naked, and has a fully-grown tiger as a companion. The pipes attract a mute teenage village boy to Tiger Boy's side (possible echoes of the Pied Piper). However, he's not actually magical - it's a feudal, post-holocaust world. (He's certainly not immortal either.)
The Elenium—A young girl ,the Goddess Aphrael, who seemingly doesn't talk but does play the flute is named Flute by our heroes.
The Lion, the Witch and the Wardrobe—The faun Mr. Tumnus (the first Narnian we meet) played a flute lullaby to Lucy on her first trip to Narnia.
Xanth—Chester Centaur's magical talent is to manifest and play a magical flute.
The Rat Piper in The Amazing Maurice and his Educated Rodents (the real one, not the stupid-looking kid) works very hard at maintaining this image. Maurice and Keith trade on his reputation.
The Blind Idiot God Azathoth in the Cthulhu Mythos enjoys himself some flute music, which undoubtley be at least extremely unpleasant to human listeners.
The Piper of The Keys to The Kingdom, who is based on The Pied Piper of Hamelin, uses his pipes to control children and rats.

Live-Action TV

Fraggle Rock — Cantus played a magical forked pipe.

Mythology

Classical Mythology—The Greek god Pan could induce fear and panic with his pipes.
Native American US' Southwest—Kokopelli is this, mixed with the fertility role, thus giving a new meaning to his flute

Tabletop Games

Dungeons and Dragons -- Satyrs have pipes that they can use to create magical effects.

Theatre

Fiddler on the Roof—The titular fiddler is the embodiment of the Jewish spirit.

Opera

The Magic Flute—Naturally, and there are also magic bells involved.

Video Games

Fire Emblem Elibe—Nils plays the flute, allowing one character to make an extra move, and later in the game, providing status buffs.
The Legend of Zelda series—Link, although he himself is not very mysterious since he is the player-character. His instrument also varies from game to game: recorders, ocarinas, pan pipes, etc. Sometimes, though, such as in The Legend of Zelda: A Link to the Past, Link gets his flute from a character who plays this trope straight.
Mushihime-sama BUG PANIC!—A mysterious girl who appears in the cutscenes named Sora
Ni GHTS—The eponymous character herself plays the invisible flute.
Okami—Waka, who is also named after a form of Japanese poetry. His appearance is always announced by the sound of a flute.
Seiken Densetsu 3—A magic flute summons a big goggles-wearing turtle at beaches.
Super Mario Bros 3—A magic whistle can be used to skip whole worlds.
Dynasty Warriors—Zhen Ji's primary weapon is a magic flute that she also uses to hit people over the head.
Final Fantasy IX—Eiko, a White Mage and summoner, can use flutes as weapons.

Western Animation

Looney Tunes—A few shorts have parodied The Pied Piper:
- Porky Pig played the Piper in a couple of cartoons. In one he has to contend with a cat angry with him for ridding Hamelin of rats.
- Sylvester tried to make a flute to capture Speedy Gonzalez and friends. Also, Sylvester Jr. found that he could attract different animals by adding holes to the flute.
Shrek Forever After—The Pied Piper is a bounty hunter, his flute adjustable to whatever creature he wanted to hypnotize (in this case, ogres).
The Smurfs and the Magic Flute—Peewit stumbles upon the magic flute of the Smurfs that makes whoever listens to it dance to its tune. It ends up in the possession of a thief named Matthew McCreep, who uses it to make people pass out from the dancing so he can rob them.

Real Life

The Japanese shakuhachi is strongly associated with the Fuke sect of Zen Buddhism, who used the instrument as part of their meditative process. When the Meiji government cracked down on the previous bakufu and all associated religions, they specifically attacked the practice of playing the shakuhachi.