Made of Magic

When something or someone is literally Made of Magic, or at least an equivalent.

Not to be confused with Made of Phlebotinum, where 'magic' makes the setting work at all (it does count if the setting itself is Made of Magic). You may occasionally find someone to be Made Of Evil Magic. A Place of Power is usually Made of Magic, as well as many supernatural beings.

Creatures that are Made of Magic may in fact be a Pure Magic Being, or an Energy Being, depending on whether the setting has more of a Science Fiction or a Fantasy flavor. In a Science Fantasy setting, the creature might be both.

Examples of Made of Magic include:

Anime and Manga

The entire Shinigami-world of Bleach is made from 'spirit particles', making those skills that rely on absorbing said particles many times more powerful. There's some fairly nifty scenes where you can see nearby walls and buildings slowly dissolving as the particles are absorbed and redirected into an attack...
The Living Programs (including Wolkenritter and Materials) in the Lyrical Nanoha series are constructs made out of magical energy. Also, the Unison Devices are probably thus, too.
The Magical World, and most residents in Mahou Sensei Negima, are Made of Magic. This makes them vulnerable to beings able to manipulate their substance. (And gives the heroes a resistance since they're made of "mundane" matter.)
Certain beings (phenomenons, individuals) in A Certain Magical Index are made of AIM-field. Most of the time they spontaneously come into existence. You can't have so many Espers (and Mages) living so close together, all practicing so much crazy powers, and not expect some feedback.
The Servants (Heroic Spirits) in Fate/stay night and Fate/Zero are made of Mana, and will disappear when their Master can no longer channel Mana into them such as when Lancelot kills Kariya by overdraining the latter's Mana. A lesser version of this are the Homunculus such as Irisviel and her daughter Ilyasviel who are walking circuits of magic in the shape of human beings.
In Dragon Ball, this is said to be the origin of Majin Buu, who was conjured into existence by an extremely powerful wizard named Bibidi.

Comic Books

Green Lantern Hal Jordan recreates his destroyed hometown of Coast City using his power ring.

Fan Works

In That Was Part of the Plan, the second of a series of Harry Potter fics by LysandraLeigh, it's revealed by a character who claims to have been there at its creation that Hogwarts was originally an entirely conjured structure, capable of reconfiguring itself as needed for defense or other purposes. However, after a couple generations this was forgotten, and new wings and expansions were added to it with mundane materials, limiting its ability to restructure itself and weakening its wards.
So-called "solid energy" projections created by Doug Sangnoir in Drunkard's Walk seem to be this, and vanish once he stops sustaining them.

Literature

Everything in the magical world in The Dark Lord of Derkholm contains magic in it to the point that people from another world were digging up dirt in that world and smuggling it into their magic-less world to do magic (and make a lot of cash).
Discworld isn't made of magic, but it is explicitly noted in the novel The Last Hero that without magic the turtle would die, the seas run dry, the sun burn out and crash, and the elephants would cease to exist altogether. And that would happen within a few seconds of magic ceasing to exist.
- A more direct example is the tower Coin constructs in Sourcery which is literally willed into being from magic made solid:

Coin: It is made of magic. Raw magic. Solidified. Curdled. Renewed from second to second. Could you imagine a better substance to build the new home of sourcery?

The Princess Series features the Seven Dwarves as living representations of elements, the last of which is magic.
In The Dresden Files, the Nevernever and all it's inhabitants are this.

Live-Action TV

In Monty Python's Flying Circus, The Amazing Mystico and Janet put up blocks of flats using the power of hypnosis.

Of course they're safe. There's absolutely no doubt about that. They are as strong, solid and as safe as any other building method in this country. Provided of course people believe in them.

Tabletop Games

The world of Exalted is the great grand master pimp-daddy of this trope, and takes it for all it's worth. Everything, from the lowliest mortal, to the Unconquered Sun, from the most solid center of Creation, to the pure chaos of the Wyld, is made of Essence.
Dungeons & Dragons
- Outsiders are beings from Alternate Dimensions called the Outer Planes and are made from their respective magical birthplaces. Pre-4th edition, they were:
  - Fiends as a whole are made from the lower planes, with Demons, Yugoloths, and Devils coming from the Abyss, Gray Waste, and Baator respectively.
  - Angels and other celestial beings come from the upper planes, with Archons, Guardinals and Eladrin coming from Mount Celestia, Elysium, and Arborea respectively. Angels uniquely can come from any of the celestial planes, and have no infernal counterpart.
- Outside even the Outer Planes lies the Far Realm, which can be considered the home of Pure Alien magic.
- Living Spells, as the name suggests, are spells that have taken on a life of their own.
- Grisgols are made of magical items assembled as a humanoid body.
Everything (save for Planeswalkers) in Magic: The Gathering. According to Wizards' Magi Babble, every card you play are Mana-based magical copies of beings existing on the other side of Blind Eternity. (Prior to this Retcon they were the real thing, summoned and enslaved by your might. Guess that made some players feel bad.)

Video Games

Ledgermayne, the Seventh Lord of Chaos from Adventure Quest Worlds, is a being of chaorrupted mana incarnate.
Espers in Final Fantasy VI, which was a very bad thing since The Empire used them as weapons material.
Every entity that exists in the UG in The World Ends With You is made of matter called Soul.
In Valkyrie Profile games, the Valkyrie employ souls of dead warrior re-materialized in the world with Divine Materialization Energy. So while in the world, they are made of Divine magic. That this includes the Valkyrie is an important point in the game, beyond being able to heal her with things that heal materialized Einherjars.
Heroes of Might and Magic III: Armageddon's Blade featured Magic Elementals, who were Elemental Embodiments of magic.

Western Animation

Aku, the Big Bad of Samurai Jack, is made of a piece of the elemental chaos of the universe. Also, Jack's sword is made of the goodness of his father.