As stated at Grognardia.blogspot.com, the mind flayer (which first appeared in the first issue of The Strategic Review in the Spring of 1975) was inspired by H.P. Lovecraft's Great Old One Cthulhu, to which they bear more than a passing resemblance. When Gary Gygax (one of the co-creator of Dungeons and Dragons) was asked about this question in a Q&A thread at ENWorld a few years ago, he had this to say:
”The mind flayer I made up out of whole cloth using my imagination, but inspired by the cover of Brian Lumley's novel in paperback edition, The Burrowers Beneath.”
Psionic tyrants, slavers, and interdimensional voyagers, mind flayers are insidious masterminds that harvest entire races for their own twisted ends.
Mind flayers, also called illithids, are the scourge of sentient creatures across countless worlds. Four tentacles snake from their octopus-like heads, flexing in hungry anticipation when thinking creatures come near.
In eons past, illithids controlled empires that spanned the planes. They subjugated and consequently warped whole races of humanoid slaves, including the githyanki and githzerai, the grimlocks, and the kuo-toa. Conjoined by a collective consciousness, the illithids hatch plots as far-reaching and evil as their fathomless minds can conceive.
Since the fall of their empires, illithid collectives on the Material Plane have resided in deep in the Underdark.
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