I first heard of Illithids or Mindflayers all the way back in the very first session of DnD I ever played.
I heard them talking about psioniscists (a psychic character class), which piqued my interest and then they mentioned the tentacled masters of psionic power and the image was burned into my imagination.
You see, Mind flayers like to eat brains with their tentacles. They are cthonic beings who loathe sunlight and destroy their prey with psychic blasts. And they are hermaphroditic, so nothing will stop their reproduction, except, foolhardy adventurers.
That's DnD, right there.
Plus, they reminded me of the Squid Face figure from Kenner's Star Wars toy line. So they had that going for them.