Examples

The Endless from Sandman.
Green Lantern: The Green Lantern Probert was known as "The Bad One." He's one of two anti-hero Green Lanterns introduced in the '90s (three, if you include the five minutes Lobo wore one.
Played With: "The Fantastic Four" fits this naming format, but sounds goofy, harmless, and overblown. This is a really bad assumption to make.
Doctor Strange has The Ancient One: The most powerful sorcerer of his generation — or any generation — for six hundred years.

The Great Old Ones in H.P. Lovecraft's Cthulhu Mythos.
Wheel of Time: The Dark One
The Lone Power of Young Wizards, sometimes referred to as "The Lone One", although It has many names.
The Dark Tower: The Crimson King.
The Unholy. A character from the novels of Vampire: The Requiem. She's pure Nightmare Fuel for other vampires.
The White Witch from The Chronicles of Narnia.
The King in Yellow.

Angel: Quor'toth is a hell dimension that's so nasty there are no portals to it, cosmic holes have to be punched through to travel back and forth there. The natives of that realm are so terrified of one being there that they know it only by the name of "The Destroyer". When the gang learn it's on its way to Earth, there are several comments from characters commenting that anyone called that has to be someone you don't want to meet. It turns out to be Angel's kidnapped son, Connor.
Buffy the Vampire Slayer:
- The Anointed One. ... is a subversion, because he's pathetic and is quickly killed by Spike.
- The other other Old Ones.
Rule of Three: The First Evil.
The First Ones, from Babylon 5, though those who weren't Shadows or Vorlons weren't really that bad.
Aerys "The Mad King" Targaryen of Game of Thrones, who thought it was a jolly jape to off people by burning them to death.

Trinités : The Devoured Ones.
The Dark Eye: The Nameless One, the god of a secret (and evil) cult.
Warhammer 40,000: The Unclean One, The Nightbringer, The Deceiver, The Void Dragon, The Outsider.
Warhammer: The other other other ... Old Ones.
Magic: The Gathering: The Doubtless One, Nameless One, Soulless One, Reckless One, Heedless One.
Yu-Gi-Oh!: Exodia the Forbidden One.

Toys

Planescape: Torment: The Nameless One, also known as The Broken One. Also, the Transcendent One.
Demon's Souls — The Forgotten One, and the Old One.
Bayonetta has Father Rodin, The Infinite One, as a Bonus Boss.
A Bonus Boss of Castlevania: Lament of Innocence is also named The Forgotten One.
The Old Gods from Warcraft. The Faceless Ones from the same franchise. Also, we almost forgot The Forgotten Ones.
StarCraft — The Voice in the Darkness, also known as Lord of the In-Between Places, the Living Heart of the Void, and the One True God.
Spellforce: The Dark One.
Quest For Glory IV: The Dark One, too.
Mass Effect 2: The Illusive Man.
Star Control (not) 3: The Eternal1s.
The Last Remnant: The Fallen. Oh, and The Lost.
BlazBlue: It's advisable to stay well clear of anyone referring to themselves as The White Void.
Throughout the Bonus Dungeon of Baldur's Gate 2: Throne of Bhaal, Bonus Boss Demogorgon is only referred to as "The Imprisoned One"; nobody speaks his actual name up till the very end.
Kingdom Hearts: Birth by Sleep — The Mysterious Figure (The Unknown in Japan, which is just as bad if not worse). There's also The Iron Imprisoner, The Infernal Engine, the titles of all Organization XIII members are phrased in this manner, The Armored Controller (one of Xemnas' forms), and The Lingering Will.

Real Life

Yellow Fever.
In Ancient Greece, certain soldier types were referred to in this way. Heavy infantrymen were known as "hoplites", which is most accurately translated "the equipped ones".
Byzantine heavy cavalrymen were called "kataphraktoi" - "the armoured ones".
According to Herodotus' Histories, the Persian army had "The Immortals", an troop of ten thousand elite soldiers named so because as soon as one man died or retired, he was replaced.

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