Supposedly, Mind Flayer society revolves around the Elder Brains. Every Illithid colony is said to have one guiding its actions. Yet this crucial element of Mind Flayer society never get an entry in the core rulebooks! In 2nd, 3rd and 4th Edition, only Mind Flayers appear in the Monster Manual - the Elder Brains are left out! WHY, in Gith's name? How am I supposed to have the PC's overthrow a Illithid colony if I don't have stats for the head honcho...? It'd be like stating that every Kolbold tribe was ruled by a Chromatic dragon, then not including any Chromatic dragon stats. (There had better be Elder Brain stats in that new Underdark book, or I'm going to have a fit of Barbarian rage...) Incidentally, when were Elder Brains added to the game and given this central role? I don't think they were in 1st Edition, but I can't swear to it.
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As far as I can tell, elder brains were first mentioned in the 2nd edition Monstrous Compendium. They weren't given statistics there because they were non-combatants. The mind flayer entry specifically said they didn't attack, but they could warn mind flayers of the presence of intruders within their telepathic range.
Bruce Cordell, in The Illithiad, decided to flesh them out and give them the ability to attack people psionically; thus, statistics were needed for the first time, which that book provided. In third edition, psionics in general were mainly limited to the Psionics Handbook, Expanded Psionics Handbook, and Complete Psion, and with space at a premium, the statistics for them were delayed.
You can, of course, encounter mind flayers in situations where you won't have to fight the elder brains, so you don't actually need them in the core rules. You can fight solitary or small groups of illithids manipulating events in a human or dwarven city from behind the scenes, for example, or infiltrate illithid outposts too small to have an elder brain.
It is weird, though, that the only places you'll find their stats in 3rd edition are Underdark, Lords of Madness, and (for the Thoon ones) the Monster Manual V. It would have made sense to put them in the Expanded Psionics Handbook. I guess they stuffed so much else in the psionics books that Underdark was the first place they had room. Lords of Madness is roughly the 3rd edition equivalent of The Illithiad, so it makes sense there as the source to go to get a more in-depth look at mind flayers.
For 4th edition, you'll either have to convert them yourself, find a conversion someone else has done, use mind flayers in situations where they don't have their elder brains available, assume elder brains are noncombatants, or wait until WotC provides you with 4e stats for them (probably in Underdark, as in 3e).