Eldritch Being

"The Old Ones were, the Old Ones are, and the Old Ones shall be. Not in the spaces we know, but ‘between’ them, They walk serene and primal, undimensioned and to us unseen."

- H. P. Lovecraft, "The Dunwich Horror".

A term popularized by the Cthulhu Mythos, the word "eldritch" means something like "coming from a foreign realm". These beings are the strangest the universe has to offer; even for alien standards they're otherworldly. They are usually extremely powerful and typically display inexplicable and supernatural abilities.

They may manifest themselves either corporeally or noncorporeally. In some cases, their physical manifestations constitute a mere shadow of what they truly are, and they may have several avatars.

Often, beings such as these tend to be neutral towards lesser life forms, but they might be extremely malevolent and pure evil (e.g. Nyarlathotep, It, the Great Intelligence, Mind Flayer, Eihort and Y'golonac), or in rare cases they might be friendly (e.g. Mr. Nobody).

Examples
"It was a terrible, indescribable thing vaster than any subway train—a shapeless congeries of protoplasmic bubbles, faintly self-luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter."

- William Dyer describing a Shoggoth.

Keep in mind that all examples are, at least to some extent, subjective, as there's no clear line between "eldritch" and simply "alien". The idea of what qualifies as an "eldritch being" ought to vary from person to person.

Literature

 * Qu (All Tomorrows)
 * Cthulhu Mythos:
 * Great Old Ones (e.g. Cthulhu, Tsathoggua, etc.)
 * Outer Gods (e.g. Azathoth, Nyarlathotep, etc.)
 * Shoggoth
 * Colour Out of Space
 * Elder Gods
 * Flying Polyps
 * Hounds of Tindalos
 * Space-Eaters
 * The City and the Stars:
 * The Mad Mind
 * Vanamonde
 * Humanx Commonwealth:
 * The Great Evil
 * Vom
 * The Hog (Carnacki, the Ghost-Finder)
 * Pan (The Great God Pan)
 * Monstrous Sawfly (The Residence at Whitminster)
 * Anabis (The Voyage of the Space Beagle)
 * Thing (Who Goes There?)
 * IT/Pennywise (Stephen King's IT)
 * Xeelee (Xeelee Sequence)

Comic Books

 * DC:
 * Anti-Monitor
 * Dark Giants
 * Star Conquerors
 * Fifth-Dimensional Imps
 * Marvel:
 * Many-Angled Ones (e.g. Shuma-Gorath, etc.)
 * Galactus
 * Gah Lak Tus
 * Amatsu-Mikaboshi
 * Glory
 * Oblivion
 * Infinites
 * Hunger
 * Phoenix
 * Knull
 * M'Gubgub
 * Gauna (Knights of Cydonia)
 * Hellstar Remina (Hellstar Remina)
 * Nova (Freezing)
 * Getter Emperor (Getter Robo)
 * Hellboy:
 * Ogdru Jahad
 * Ogdru Hem
 * Wolochs (Valérian and Laureline)

Films

 * Creatures (Bird Box)
 * Omega Mimic (Edge of Tomorrow)
 * Event Horizon (Event Horizon)
 * Ultimate Evil (The Fifth Element)
 * King Ghidorah (Godzilla: The Planet Eater)
 * Ogdru Jahad (Hellboy)
 * Calvin (Life)
 * Marvel Cinematic Universe:
 * Dormammu
 * Ego the Living Planet
 * Dweller-in-Darkness
 * Celestials
 * Thing (The Thing)

Television

 * Babylon 5
 * Shadows
 * Thirdspace Aliens
 * Doctor Who:
 * TARDIS
 * Animus
 * The Great Intelligence
 * Nestene
 * Sutekh
 * Fendahl
 * Great Vampires
 * Eternals
 * Fenric
 * Reapers
 * The Beast
 * Abaddon
 * Torajii
 * Weeping Angels
 * Midnight Entity
 * The Flood
 * House
 * Akhaten
 * Boneless
 * Kasaavin
 * Insects (Lexx)
 * Alioth (Loki)
 * Darkseid (Smallville)
 * Star Trek:
 * Doomsday Machine
 * Crystalline Entity
 * God
 * Q
 * Medusans
 * Species 8472
 * Borg
 * Mind Flayer (Stranger Things)
 * Supernatural:
 * Angels
 * Leviathans
 * Yokoth and Glythur
 * The Darkness
 * The Shadow

Cartoons

 * Ben 10: Ultimate Alien:
 * Lucubra
 * Dagon
 * DC Animated Universe:
 * Unity (Superman: The Animated Series)
 * Old Ones (Justice League)
 * Futurama:
 * Yivo
 * Brain Spawn
 * Four-dimensional Space Whale
 * Final Space:
 * Mooncake
 * Arachnitects
 * Titans
 * Invictus
 * Werthrent
 * Bill Cipher (Gravity Falls)
 * Space Monsters (Gunbuster)
 * Anti-Spirals (Gurren-Lugann)
 * Big Bad (Hanazuki: Full of Treasures)
 * Sleeping Beast (He-Man and the Masters of the Universe)
 * Angels (Neon Genesis Evangelion)
 * Black Mass (Samurai Jack)
 * Evil Entity (Scooby-Doo)
 * Cluster (Steven Universe)
 * Dark Ones (Super Robot Monkey Team Hyperforce Go!)
 * Unicron (Transformers)
 * Wander over Yonder:
 * Black Cube of Darkness
 * Space Demons
 * Myrtle

Tabletop Games

 * Dungeons & Dragons:
 * Aboleths
 * Beholders
 * Gibbering Mouther
 * Illithids
 * Elder Evils (e.g. Atropus, Father Llymic, Hulks of Zoretha, Leviathan, Pandorym, Ragnorra, Sertrous, Kyuss, Zargon, etc.)
 * Magic: The Gathering:
 * Marit Lage
 * Eldrazi
 * Pathfinder:
 * Rovagug
 * Qlippoth
 * Dominion of the Black
 * Rifts:
 * Splugorth
 * Vampire Intelligence
 * Warhammer:
 * Chaos Gods
 * C'tan
 * Tyranids

Video Games

 * Great Ones (Bloodborne)
 * Vault Monsters (Borderlands)
 * Lavos (Chrono Trigger)
 * Brethren Moons (Dead Space)
 * Icon of Sin (Doom Eternal)
 * G-Man (Half-Life)
 * Flood (Halo)
 * Kirby:
 * Dark Matter
 * Fecto Elfilis
 * Voidborn (League of Legends)
 * Titans (LittleBigPlanet)
 * Mass Effect:
 * Reapers
 * Leviathans
 * Thorian
 * Metroid:
 * Phantoon
 * Emperor Ing
 * Gorea
 * Phaaze
 * Leviathan
 * X Parasite
 * Giygas (Mother/EarthBound)
 * Pokémon:
 * Arceus
 * Deoxys
 * Ultra Beasts
 * Necrozma
 * Eternatus
 * Sonic the Hedgehog:
 * Solaris
 * Time Eater
 * StarCraft:
 * Zerg Overming
 * Xel'Naga
 * Star Wars: The Old Republic:
 * Sel-Makor
 * Darth Nihilus
 * World Razer
 * Lotek'k
 * Stellaris:
 * Dimensional Horror
 * Stellarite Devourer
 * Turok:
 * Primagen
 * Oblivion
 * Warcraft:
 * Faceless
 * Forgotten Ones
 * Old Gods
 * C'Thun
 * Yogg-Saron
 * N'Zoth
 * Y'Shaarj
 * Sha
 * Void Lords
 * Warframe:
 * Sentients

Others

 * Moon (Local 58)
 * SCP Foundation:
 * He-Who-Made-Dark
 * He-Who-Made-Light
 * Neverwere
 * Old Gods (e.g. Scarlet King, Yaldabaoth, Mekhane, Hanged King, etc.)
 * Pattern Screamers