Dungeons & Dragons (1974-1976)
Mind flayers first appeared in the official newsletter of TSR Games, The Strategic Review #1, Spring 1975. Here, the mind flayer is described as "a super-intelligent, man-shaped creature with four tentacles by its mouth which it uses to strike its prey." When it hits prey with a tentacle, the tentacle penetrates to the brain and draws it forth, allowing the monster to devour it. A mind flayer's major weapon is given as the Mind Blast, a 5-foot radius wave of "PSI force" which affects each opponent differently based on how intelligent it is; possible effects include permanent insanity, rage, confusion, coma, and death. They were also included in the Eldritch Wizardry supplement, for the original (white box) Dungeons and Dragons game (1976), wherein they are described as super-intelligent, man-shaped creatures of great (and lawful) evil, with tentacles that penetrate to the brain and draw it forth for food.
Illithid

Funny that these are also in Demon's Souls, and in a way Dark Souls.