"The Width of a Circle" features David Bowie "encountering" an Eldritch Abomination. Consensually, no less. (The Seventies were a weird time.)
"The Man Who Sold The World" and "The Supermen" are more orthodox examples of this trope. They're all from the same album, too (The Man Who Sold the World)!
"The Thing That Should Not Be" by Metallica is about such a creature, and, quite obviously, is directly inspired by Lovecraft.
Also "The Call Of Ktulu" (though it's an instrumental).
In Guitar Hero, Metallica's "Metallifacts" video for "The Thing That Should Not Be," it also lists "All Nightmare Long" and "Ride The Lightning" as being inspired by H.P. Lovecraft's stories, specifically, "Shadow Over Innsmouth."
In Savatage's song "Hall of the Mountain King", the titular Mountain King is an eldritch abomination.
Much of Current 93's and David Tibet's work has heavy eldritch-apocalypse overtones. Black Ships Ate The Sky & The "Inmost Light" Trilogy in particular.
The spoken lyric to I Have A Special Plan For This World, written by horror author Thomas Ligotti, has several references to these, the most blatant perhaps being the "sardonic spirit" that speaks to the narrator about death... or the narrator himself, depending upon your interpretation.
Blue Öyster Cult is very fond of including these. Their entire Imaginos album plays with it and the song E.T.I. (Extra Terrestrial Intelligence) offers these lyrics:
"I'm in fairy rings and tower beds/Don't report this three men said/Books by the blameless and by the dead/King in Yellow, queen in red...all praise/he's found the awful truth..."
The song Harvest Moon from their Heaven Forbid album features the following lyrics towards the end:
"I sense the darkness clearer/I feel a presence here/A change in the weather/I feel some evil here/I hear some frightful noises/I don't go out at night/Since Bobrow's youngest daughter/Disappeared from sight/I know they'll find her some day/They find them all that way..."
And in the song Sub Human, which appears in two versions(Secret Treaties and Imaginos:
"Oyster boys are/swimmin' for me/Save me from the/Death-black creatures..."
Harvester Of Eyes seems to be sung from the perspective of an Eldritch Abomination:
Nile writes about a few of these in their songs, sometimes referring to Egyptian deities, and sometimes to Lovecraftian ones. The best example in their music is from "Von Unaussprechlichen Kulten" which is essentially a retelling of the story "Dagon" by Lovecraft, only this time involving serpent folk: "I hath dreamed bleak and grim dessolate visions of the pre-human serpent volk, and communed with long dead reptiles, silently watching throught the ages, in cold curious apathy, the unending sorrows and sufferings of an abysmal human kind."
The title track of Vektor's Black Future album seems to deal with an entity akin to this that also acts as The Virus and a Lotus-Eater Machine.
Pretty much everything by Internal Suffering either has something to do with one of these or messing around with magic related to them.
Being heavily inspired by Event Horizon, the storyline for Luca Turilli'sProphet of the Last Eclipse seemed to be going in this direction. The demons could likely qualify, as well as anyone touched by The Black Portal. Though Dark Is Not Evil in the latter case. And if Riders of the Astral Fire is any indication, those are only a warmup for what's coming. Unfortunately the sequels never happened.
In the Talking Heads song "Air" the very air itself is an Eldritch Abomination. Wow. "Air hit me in the face. I run faster and faster...into the air. And I say to myself, 'What is happening to my skin? Where is that protection that I needed?' Air can hurt you too, air can hurt you too. Some people say not to worry 'bout the air. Some people never had experience with air. It can break your heart...."
"Azathoth" by Proto-Prog group Arzachel, which is about the Lovecraftian god of the same name.
The titular universe-devouring force in "The Great Annihilator" by Swans probably qualifies.
"Iron Butterfly Theme", an instrumental piece about the birth and death of an "iron butterfly".
