I can't limit myself to a single thing about any edition, so this isn't so much a "most" for me as it is a "here's one thing that tickles my fancy about each!" listing:
Original D&D: Looking back at the psionics introduced in
Supplement III: Eldritch Wizardry, I'm struck my just how alien they were. You actually
lost abilities (e.g. spell slots, Charisma points, etc.) in order to gain psionic powers. While it's obviously an early attempt at maintaining game balance, it creates an in-character effect where utilizing those powers seemingly burns out part of your brain, isolating you from normal humanity as you tap into a weird, supernatural power...
AD&D 1st Edition: It might be a bit idiosyncratic, but I'm still struck by how the reworked paladin in
Unearthed Arcana can improve almost all of their ability scores (I think all but Wisdom) as they level up. Literally, they get to increase their ability scores by a fractional value, and when that value exceeds 100, the score goes up by 1, to a maximum of 18/00 (the fractional values don't add anything, except for Strength, which uses the "exceptional Strength" rules as normal). The cavalier has this too, but for only four of the six ability scores (I can't recall which one the paladin gets that they don't). It's an exceptional boost to what's already one of the strongest classes you can take.
BECMI: I can't remember if it was laid out in the
Immortals Set or
Wrath of the Immortals, but the idea that after you became a Hierarch Immortal, you could give up your Immortality to start again as a level 1 character, and if you worked your way up to Hierarch Immortal a second time you'd be taken beyond the multiverse to become one of the "Old Ones," always struck me as extremely cool. It was basically the New Game+ of Dungeons & Dragons, with the best ending being unlocked if you could pull it off.
AD&D 2nd Edition: Assuming I recall correctly, there's a little tidbit of a rule tucked away in
DMGR4 Monster Mythology (I think in the introduction) where it gives prayers asking for divine intervention a 1% chance of succeeding (and once one of those rolls does succeed, it won't anymore; the idea being that your god won't keep helping you if you continue to find yourself in situations where you need their direct assistance). I love this idea, that there's always some minor chance (so long as you have a patron deity) that no matter how bad things look, you can always use this "roll of last resort" to ask your god to step in and help you out.
D&D 3rd Edition: I'll nominate the 3.0
Dungeon Master's Guide here. While I know a lot of people disregard the 3.0 Core Rules in favor of their 3.5 counterparts, there were a lot of optional rules in the 3.0 DMG that - as I recall - didn't make it into the later revision. For instance, there's a (quite complicated) rule about hitting targets other than who you were aiming at when you miss with a ranged attack. That's the sort of verisimilitude that I like to contemplate, even if the implementation was a bit too rules-heavy.
D&D 4th Edition: It might not have been called the Plane of Shadow anymore, but it was nice to see that plane get its own boxed set in
The Shadowfell: Gloomwrought and Beyond. Heck, it was nice to see a boxed set again that wasn't a starter set for learning how to play the game.
D&D 5th Edition: It's more "D&D Next" than 5E proper, but I got a kick out of seeing Abdel Adrian again in
Murder in Baldur's Gate. He didn't get the send-off I felt he deserved, but it was nice that he got one at all.
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