Old/Classic D&D: Honestly, most of what I like best about Classic is just stuff that AD&D broke and WotC just kept grinding further into the dust. But if I wanted to get specific, I would point out Race as Class meant that playing a nonhuman character meant something. Name Level Subclasses mark 9th level as a substantial change in your character's role in the campaign world. Divine Ascension as the ultimate endgame.
Advanced Dungeons & Dragons: Multiclassing. Monks. Assassins. Oriental Adventures. As little regard as I have for the original AD&D... I recognize that it also laid a lot of the groundwork for everything I loved about later editions.
Advanced Dungeons & Dragons, Second Edition: If you include the Player's Option rules, this is my absolute favorite edition of D&D; if you don't include them, it drops to the bottom half. Everyone else has already said the campaign settings, but it really can't be said enough. Kits. The PHBR series in general, but especially Humanoids, Priests, Paladins, and Bards.
Dungeons & Dragons Third Edition and 3.5 Revision: I really like Feats and Skills. I like that basic adventuring abilities are part of that skill system instead of exclusive class features. Spontaneous spellcasters. Savage Species, Expanded Psionics Handbook, Book of Nine Swords, and Unearthed Arcana. I can take or leave the setting as a whole, but Races of Eberron and Magic of Eberron.
Pathfinder: The non-core classes in PF are way better than the non-core classes in 3.X and they actually (most of them) got full support going forward. Third-party materials for Pathfinder are head-and-shoulders better than what was available for 3.X. d20PFSRD.com. Class archetypes. Dreamscarred Press versions of psionics and martial. Pathfinder Unchained.
Dungeons & Dragons, Fourth Edition: Healing Surges. A/E/D powers. Primal and Shadow as independent power sources. Psionics mechanics. Paragon Paths and Epic Destinies as additions to your class instead of replacements for it, harkening back to BECMI's name level subclasses. The handling of races is better than it's been since before AD&D separated race and class. edit: Oh, hey, also monster design; monsters don't just have attacks and spells, they have unique, defining powers.
Dungeons & Dragons, Fifth Edition: Advantage/Disadvantage. The new Feats are amazing compared to previous versions. Spell scaling using higher-level spell slots. Every class having mandatory subclasses that you can specialize in.