There are many musical references to Cthulhu, especially in the genres of Heavy Metal, Gothic Rock and Folk music.
Bal-Sagoth: "Shackled to the Trilithon of Kutulu" from The Chthonic Chronicles
Beatallica, a spoof band combining Metallica tracks with songs from The Beatles likewise references Cthulhu in their song "The Thing That Should Not Let It Be", from their A Garage Dayz Nite EP. The song is a combination of "The Thing That Should Not Be" by Metallica and "Let It Be" by The Beatles.
British progressive rock band Caravan has a song "C'thlu Thlu" on their 1973 album For Girls Who Grow Plump in the Night.
Clutch mentions Cthulhu's "red-headed step-child" in "Circus Maximus" off their Robot Hive/Exodus album.
Cradle of Filth has a song called "Cthulhu Dawn" on the album Midian. The album Nymphetamine 2004 has several references to Cthulhu including chants of "Ia! Ia! Cthulhu fhtagn!" in both "Mother of Abomination" and "Satyriasis". R'lyeh is mentioned in the lyrics of the song "English Fire" on the same album. They also have an album titled "Lovecraft & Witch Hearts". Songwriter Dani Filth treats Cthulhu as a female entity.
The Darkest of the Hillside Thickets, a Canadian rock band, makes frequent (and usually tongue-in-cheek) references to Cthulhu and other members of the Lovecraft mythos, going so far as to have albums with names like Cthulhuriffomania! and Cthulhu Strikes Back. They also produced Let Sleeping Gods Lie, an album made with Wizards of the Coast to promote the new edition of the Call of Cthulhu role-playing game.
Mark E Smith of The Fall based his track "The Horror in Clay" on his spoken-word album "The Post Nearly Man" on Lovecraft's "The Call of Cthulhu".
Fields of the Nephilim featured references to Cthulhu, particularly in songs on the album The Nephilim.
A quotation from "The Call of Cthulhu" ("That is not dead which can eternal lie, and with strange aeons, even death may die") appears on a tombstone on the cover of Iron Maiden's Live After Death album.
Epic heavy metal band Manilla Road dedicated the album Atlantis Rising to the concept of Cthulhu fighting the Norse Gods and Poseidon over the newly risen city of Atlantis.
Metallica wrote two songs referencing Cthulhu: The instrumental "The Call of Ktulu", recorded on the 1984 album Ride the Lightning, and "The Thing That Should Not Be", appearing on the 1986 album Master of Puppets. Both of these tracks also appear on the band's album with the San Francisco Symphony Orchestra, S&M. The band's late bassist Cliff Burton was an avid Lovecraft fan. 
Many of Morbid Angel's songs reference Cthulhu and the Cthulhu Mythos. Such include on the album Abominations of Desolation the songs on there are Azagthoth (referring to Azathoth), Angel of Disease (which mentions Cthulhu, Ancient Ones, Shub-Niggurath, and the Elder Gods), and The Gate/Lord of All Fevers. On the Formulas Fatal to the Flesh album, almost all the songs on there have references to the Cthulhu Mythos Also the lead guitarist is named Trey Azagthoth.
The American death metal band Nile refers to Cthulhu or related deities in various songs, with some of their work related to Lovecraftian fiction, including the album title Amongst the Catacombs of Nephren-Ka (from "The Outsider") and the song "Von Unaussprechlichen Kulten". In addition, the album Ithyphallic includes references to Cthulhu in the song "What Can Be Safely Written". Most of the band members, particularly Karl Sanders, admit to being great fans of Lovecraft's work.
Samael, a black metal band from Switzerland, had an instrumental track named "Rite of Cthulhu" on their album Worship Him.
Tom Smith has written several songs which feature Cthulhu, including a parody of the song "Hakuna Matata" (from the Disney film The Lion King) entitled "Cthulhu Fthagn". The song is primarily sung by Dagon and Abhoth, gods in the Cthulhu mythos. Others include "House at Cthulhu Corner" (Based on "House at Pooh Corner,") and "Cthulhu Lite FM."
The symphonic metal band Therion released a song named "Ctulhu" on their second studio album Beyond Sanctorum (1992). There is also a demo version of "Ctulhu" on the 2000 re-release of this album.
The Tiger Lillies performed the Song "Cult of Cthulhu" on their tour (and available on DVD) for the Lovecraft inspired tour of Mountains of Madness
The black metal band Venom's song "The Evil One" off their album Cast in Stone has a reference to Cthulhu.
The Norwegian black metal band 1349's song "From the Deeps" is about the rise of Chtulhu.