There are multiple artists with this name:
1) Goblin is an Italian progressive rock band known for their soundtrack work. They frequently collaborate with Dario Argento, most notably creating soundtracks for Profondo rosso in 1975 and Suspiria in 1977.
The group was initially named Cherry Five. Influenced by Genesis and King Crimson, their early work spawned one eponymous progressive rock record. The band changed their name to Goblin when they were called in to compose the soundtrack for Profondo rosso, rewriting most of the score originally written by Giorgio Gaslini, including the famous main theme. The film, and the soundtrack album, were huge hits.
A reshuffle in their line-up followed, and then an instrumental progressive rock album Roller, before they got the chance to work with Argento again for Suspiria. The score's nerve-jangling experimental sounds and bizarre vocals have since become legendary. Other film soundtracks and a concept album (Il fantastico viaggio del bagarozzo Mark) followed, then the score for the European version of George A. Romero's Dawn of the Dead (1978).
Despite their success, more members of the band left. The line-up was altered again, but this time they struggled to maintain their credibility. What was left of the band continued to work on further soundtracks, but there was a partial reunification for Argento's Tenebrae (1982) (although they were credited separately, not as Goblin).
In 2000, the group reformed to score the new Dario Argento thriller titled Non ho sonno (aka Sleepless). After over 22 years of absence, their return was spectacular. The soundtrack was a great success and showed the group could still compose after such a long time apart, much to the fans delight. Since that time the group has again been disbanded, amid disagreements during the production. Nevertheless in 2005, the official Goblin biography written by Giovanni Aloisio was released and an official website called Back to the Goblin. In 2007, Goblin recorded the soundtrack for Argento's follow-up to Suspiria and Inferno, titled La terza madre (aka The Mother of Tears).
They also recorded under other names, including Il Reale Impero Britannico.