From the birthplace of the universe, Lex Luthor gathered particles and pieces of galactic matter until he had enough to build a man. Like the legendary Golem who had been molded from clay, Luthor’s man-thing was molded from galactic matter, then given a form of psuedollife by an intensive bombardment of interstellar radiation focused by Luthor through his cosmic cannon. Since Luthor’s galactic Golem needed repeated infusions of this energy to survive, it would track down and destroy any object Luthor had filled with the energy, so the energy could be absorbed into his own body.
To this end, Luthor then secretly filled Superman with this hyperstellar energy and sent his Golem to hunt down the man of steel. Since Superman drew much of his power from Earth’s yellow sun, while the golem drew his from the stars themselves, Luthor felt (wrongly as it turned out) that Golem would overcome the man of steel.
After a long battle, Golem turned on his creator and Luthor was forced to send him on an endless journey into deep space. Several months later Galactic Golem returned to Earth to renew his fight with Superman but once again he was defeated.
Superman covered the Golem with molten steel over the center of Earth’s magnetic pole, which when hardened immobilized the Golem.
The second Golem was from the planet Daxam. It was in pursuit of Mon-El. It was sent to fight Superman, subdue him, and take Mon-El. Superman and the villain Paragon teamed up and defeated this Golem by destroying the small replica of the Daxam planet in his forehead, the power source.
New 52
Another Golem is seemingly destroyed by the construct of a newly decorated Green Lantern by the name of Sinestro.