Their first appearance in issue 1 of Strategic Review (1975) is little more than a physical description with accompanying powers, but the imagery is powerfully influenced by the Cthulhu Mythos. This is what makes this creature so appealing to me. Gygax revealed in an interview that he was influenced by the cover of Brian Lumley's The Burrowers Beneath, which shows a Cthonian bursting from underground. I could never shake off the impression that Cthulhu played a big part in its creation, even if unconsciously. The mind flayer's head is suspiciously similar to that Lovecraftian creature.
Given my love for Lovecraft's stories, it's no small wonder, then, that this creature should resonate so powerfully with me. In the AD&D Monster Manual 1st ed., Gygax expands on the creatures and there's a hint of ecology but with lots of room for adaptation and improvement. I always envision mind flayers as a sort of pre-historic creature that dwells in impossibly ancient ruins and underground, whose empire existed long ago but is no more. They scheme and weave plots to corrupt the surface races much like Robert E. Howard's serpent people. It's almost as easy to make them an extra-dimensional race or people from the stars that were trapped in the fantasy world wherein the adventures live.
What is your favorite D&D / AD&D creature and why? It can be a description, its powers or even its name. How did you use them in your campaigns? Where they a major plot element or just another foe to be vanquished?