Moloch first appeared as the sub-boss in Mortal Kombat: Deadly Alliance. He is an Oni from the Netherrealm, and is an ally of Drahmin.
While confined in the Netherrealm, Quan Chi confronted Moloch and Drahmin with an offer of freedom from the realm in exchange for protection from Scorpion. He explained to them that he had found a way out, and so the two excepted his offer. However, during a confrontation with Scorpion, Quan Chi attempted to escape from the Netherrealm while the two were busy fighting. Enraged, Moloch and Drahmin followed Quan Chi through the portal, but were transported to a different area of Outworld than the sorcerer.
While in Outworld, the two took refuge in the forests and fed on those who wandered to close. Upon learning of their presence, Shang Tsung enlisted their service and kept them hidden in the lower levels of his palace as an insurance policy, should Quan Chi betray him.
Eventually, Moloch and Drahmin were freed. However, when they were confronted by Scorpion, they defeated him and hurled him into the Soulnado, inadvertently protecting Quan Chi from his nemesis.
Moloch also appears in Mortal Kombat: Armageddon, however, he is a lot smaller than he appeared in Mortal Kombat: Deadly Alliance. No bio was released for Moloch in this game, so his storyline is unknown at this time.
Mortal Kombat: Armageddon

The Oni Destroyer Moloch absorbed the gift of godlike power from Blaze and was transformed into a Destroyer of Worlds. In a gesture symbolic of the new power, he slammed his fist against the pyramid, completely shattering the structure. Moloch then laid waste to Edenia, transforming it into a barren wasteland not unlike the Netherrealm. Because he destroyed the Edenian portals, however, Moloch was trapped there, a victim of his own destructive rage.