Berserk: The Idea of Evil is the reason the Berserk universe is such a crappy place to live: as long as people believe something is responsible for the evil, it exists.
Some humans in certain circumstances can choose to become Apostles, superhuman monsters whose bodies are transformed to demonic in exchange for Human Sacrifice of those most dear to them.
The mazoku in Slayers are beings of pure chaos that, as in the trope, feed on negative emotion, power black magic, and want to see the world returned to the Sea of Chaos. Fantasy RPGs like Dungeons & Dragons are an admitted influence on the setting, so it's possible they draw inspiration from that game's demons, etc.
In Bakugan, Mag Mel's armor is revealed to be this. Code Eve created it from the evil of former Big Bad Emperor Barodius and sealed him inside of it.
Janemba from Dragon Ball is made out of all the evil that was sucked out of the residents of Hell in order to purify their souls.
In Inu Yasha: The Shikon Jewel is a balance between this and Made of Good — hundreds of demon souls and one priestess soul are sealed within it.
Comicbooks
The Guardians of the Universe (masters of the Green LanternCorps) expelled all the evil from themselves in a similar manner to the race that created Armus in the Star Trek example below. Eventually, it took over the body of the guy who trained three different Golden Age heroes.
Films — Animated
Heavy Metal had the Loc-Nar as a connecting theme between stories. It could (at will? only sometimes?*) kill on touch, reanimate the dead, and cause volcanoes to erupt... in addition to tormenting teenage girls.
Loc-Nar: Look at me. I am the sum of all evils.
*The first rule of the Loc-Nar is never touch it while it is glowing.
Sephiroth in Final Fantasy VII: Advent Children. When he appears at the end of the movie, he is literally MADE of Jenova cells. He even bleeds it when cut. And when Cloud defeats him the excess Jenova cells making him up discorporate, leaving a beaten Kadaj behind.
'Mr. Shadow' in The Fifth Element is a moon composed of negative emotion.
Time Bandits by Terry Gilliam has Evil as the main antagonist. Once destroyed, a single piece/rock of him is overlooked in the cleanup, when Kevin's parents pick it up (after he warns them not to) they get vaporized.
In the 1980s Flash Gordon movie, the henchwoman General Kala's corpse visibly deflates and smokes as it turns into an oil spill.
Halloween's Dr Loomis believes Michael Myers is this. It would explain his ability to come back from each increasingly over-the-top death.
"I met him, fifteen years ago. I was told there was nothing left. No reason, no conscience, no understanding; even the most rudimentary sense of life or death, good or evil, right or wrong ... I spent eight years trying to reach him, and then another seven trying to keep him locked up because I realized what was living behind that boy's eyes was purely and simply... evil."
Literature
In The History of Middle-earth, Tolkien explains that Morgoth is not only the God of Evil, but is responsible for diffusing his essence into all parts of the physical world, thereby giving an elemental evil spin to all particles of matter and creating the problem of, well, evil. By weakening himself and corrupting ordinary matter to serve his purposes, "all of Middle Earth itself is Morgoth's Ring". Fortunately, his own body is not Made of Evil he is merely trapped in it.
The titular mini-black-hole in Angelmass balances the 'angel' particles it emits by becoming demonic itself.
The Big Bads in The Death Gate Cycle by Margaret Weis and Tracy Hickman were living avatars of evil who grew stronger in the presence of despair, rage and so forth. "I grow fat on your fear" isn't just a metaphor with them.
The Black Thing in A Wrinkle in Time is declared to be Evil, the Powers of Darkness.
Live-Action TV
The Big Bad of Lost is said to be this. One character describes him as "evil incarnate."
Andrew Wells: This whole thing... is being orchestrated by something called "The First." It's made up of all the evil in the whole world.
Star Trek: The Next Generation: Armus, the eponymous skin in "Skin of Evil", is a being made up of an entire civilization's discarded negative thoughts and emotions. He also killed Tasha Yar.
Apparently just about every enemy the Power Rangers used to fight was this trope. When purified of evil at the end of the sixth season, most simply crumbled to dust.
Except Rita and Zed, who turned into a yuppie couple.
And Divatox.
Subverted in Charmed. For the first four seasons, the Big Bad behind just about every evil being the Charmed Ones went up against was called The Source Of All Evil. Four years of Villain Decay later, however, and it turns out that "Source Of All Evil" is really just a title, and anyone in charge of the demonic underworld gets to call themselves that.
It's a straighter example than you might think, given that the actual Source isn't the demon leader in question, but rather an amorphous force that gets inherited by whoever is currently in charge of the Underworld at the time, and gradually takes them over from the inside out.
Tabletop RP Gs
In Dungeons & Dragons 2nd and 3rd editions, demons and the like are made of evil, and angels are made of good. Similarly, slaadi are made of pure Chaotic Neutral and modrons of pure Lawful Neutral, a concept even more nebulous than being made of good or evil. Anyways, this means fallen angels and risen demons still count as their original alignments for spell effects and Detect Evil.
In 3rd edition, any being with a subtype of 'evil' consisted in part of evil. Most of them were fiends (IE, outsiders with the evil subtype), which covers demons and the like, but there were exceptions.
The Warp in Warhammer 40K is made of all the emotions in the galaxy good and bad, but there's more bad than good. The Chaos gods have "good" traits that have been warped and amplified so much that to human sensibilities they become evil. For instance, Nurgle is a Friend to All Living Things— heavy emphasis on the ALL; Papa Nurgle loves his cute little parasites and pathogens, yes he does!
Videogames
The Persona 2 version of Nyarlathotep is an Eldritch Abomination literally born of Humanity's collective evil, absorbing every evil ("evil" defined as "with the intent of causing any form of harm to anyone, even yourself") act, thought and desire. As Long as There Is Evil, he is an undefeatable mass of concentrated madness, woe, and discord, eternally hungering for more power.
In the second game, there is also a toxic liquid named Kegare - the ancient Japanese word for "sin" or "filth", extracted by the New World Order from their followers in their seminars. Supposedly the process "purifies" the attendees. It is literally concentrated evil.
The elementals in MARDEK RPG: Chapter 3 include a Dark version. Due to the Sorting Algorithm of Evil, these are actually the least powerful elementals you encounter. The bestiary says that they don't attack so much as leak energy when disrupted, and that if they sit around too long they may crystallize and become Onyxes.
In Mother, Giygas was an alien with psychic powers and a particularly sharp hatred of humanity. By the time Earthbound rolls around though, his hatred and power has grown to such a degree that it literally destroys his physical body and turns him into a floating, indistinct entity of pure evil.
Final Fantasy IV gives us another example: "I am Zeromus... I... AM... THE HATRED!"
In Ōkami, every villain disperses into a dark, malevolent cloud (with glowing evil eyes) once beaten, and flows back to the Final Boss. Which is pretty fitting, considering Yami is the source of all Evil/Darkness in the setting. Interestingly, one sub-boss, Red Helm, has it in his backstory as having spontaneously sprung from the spilled blood of Orochi, a bigger bad.
As is repeatedly stated in Kingdom Hearts, the Heartless are really just walking bags of malevolence without any true minds of their own.
Vanitas fits this even better than the Heartless. He's literally made from Darkness.
Dark Chips and Nebula Gray from Mega Man Battle Network are made entirely of negative emotions somehow encoded as data.
The "Dark Presence" in "Alan Wake" qualifies for this; it's mysterious, almost unknowable, and has to attach itself to human shapes in order to be percieved at all.
Most of the Dark Gaia creatures in Sonic Unleashed seem to qualify. They're an ancient evil that seems to be the embodiment of negative emotion, causing sadness and anger everywhere, and when defeated, they dissolve into some kind of black-purple stuff and disappear. The exception are creatures possessed by Dark Gaia, such as The Dark Gaia Phoenix and Sonic himself, as they had a physical body to begin with.
The monsters of Silent Hill are literally physical manifestations of different aspects of negative emotions (or events) created by the town itself, or Alessa, while she was still around.
Noob Saibot from Mortal Kombat is the leftovers of when the first Sub-Zero (from the original game and Mythologies) died and had his soul hurled into the Netherrealm, turning him into a wraith. His whole existence is entirely defined by hatred and scheming, as anything honorable that the original Sub-Zero might have had (which wasn't much to begin with) was purged.
M. Bison from Street Fighter himself isn't really Made of Evil but the power he uses (Psycho Power) is described as being pure negativity as energy. Negative thoughts, emotions, and general hatred manifests itself as this force.
The protagonist of Prototype is composed entirely of biomass infused with the Blacklight virus. It's the main reason he can take so much punishment: he has no bones to break or organs to rupture. Taken even further when it's revealed that he is the Blacklight virus.
Whenever "Sephiroth" from Final Fantasy VII shows up in the game before the Final Battle, it's actually a clone made of JENOVA cells, which is as close to being Made Of Evil as one can get in the setting. The actual Sephiroth is also made entirely of JENOVA cells when he appears near the end, since his original mostly (he was infused with JENOVA cells as a fetus) human body was destroyed when he fell into the Lifestream in the backstory.
Web Originals
In Sailor Nothing, the MonsterOfTheWeeks are created by pulling out the evil inside a person's heart and physically manifesting it. It's noted that the nicer a person is, the less evil they let out, and the nastier the demon created is. The demons are also highly influenced by the original's personality. This mechanic is explored thoroughly. When it gets turned on the series' titular heroine, however... Well, it's not good.
As depicted in 2001, The Makuta was this, or at least claimed to be:
I am that power. I am Destruction. And I will destroy you.
Webcomics
Black Mage from 8-Bit Theater fits this description. A conversation between him and the external physical manifestation of everything evil he has ever done went something like this:
Manifestation: Hey, here's a question. I feel a complete contempt for everything and the overriding need to burn the world. Is that normal?
Black Mage: Are you filled with regret that, eventually, there won't be more world to burn?
Manifestation: In the back, yeah.
Black Mage: That sounds like my atrocities all right. Perfectly normal.
In the Samurai Jack third season two parter The Birth of Evil, an immense black essense roamed across the cosmos. A pantheon of gods managed to near-incenerate the... thing, but a (relatively) tiny piece survives, plummets to Earth, killing anything that comes close. Aeons later, it crystallises into the series' main antagonist Aku, due to the efforts of Jack's father. Whoops.
Darkwing Duck's evil side in "NegaDuck" is both this and an Enemy Without, and presumably has both a sort of normal physical structure as well as being made of evil, because it's created when Darkwing is split into his "good and evil elemental particles" that they made up for that episode. NegaDuck in that episode is even more so.
In Family Guy, Peter Griffin once purchased a Catholic toilet training book titled You're a Naughty Child, and That's Concentrated Evil Coming Out the Back of You.
In Teen Titans the demon Trigon the Terrible is referred to as the "incarnation of evil" and "source of all darkness."