Well, I'm still not talking yet about what I said I was going to talk about this week, but I'll get to that in the next few days. Rather; I want to talk about what are the specific legacies of each edition of D&D. Or rather; what are the legacies that I'm using. I don't actually play D&D per se anymore (not saying that I wouldn't, but rather that I don't and don't have any specific plans to either..) But anyone who plays any role-playing game at all owes something to the legacy of D&D, and in my case, where I'm utilizing a system that is specifically derivative of a specific version of D&D in specific ways and with specific elements; well—I owe something to pretty much all versions of D&D, even the ones that I haven't read, don't own and haven't ever played, like 4e and 5e.
For purposes of this exercise, I'm going to limit myself to the Xe convention; i.e., I'll refer specifically to 0e, 1e, 2e, 3e, 4e and 5e. This leaves out the B/X to BECMI to RC progression entirely, which in all fairness is probably the "true" descendant of 0e rather than AD&D (otherwise known as 1e and 2e.) When the Advanced was dropped from the title, 3e was specifically a development of AD&D though, not the RC, and the number highlighted that fact.
Anyway, on with the show.
0e: Other than the fact that the whole concept of the roleplaying game starts here (if you discount "proto-D&D" stuff like some of the Chainmail stuff Gygax and Arneson were working on before D&D itself was written) the specific legacy of 0e, or OD&D as it's sometimes abbreviated, is the much looser, rules-lite, GM ruling-heavy playstyle where anything could go and the GM figure out how to make stuff happen rather than some designer. There was much less content, and a very different approach to the game, the rules, and the playstyle here than what subsequently evolved to become commonplace. Arguably, the B/X game continued this playstyle. but in reality, it didn't take too long before D&D started to resemble AD&D more than OD&D in terms of how the game was designed and presented. There's a reason that the OSR movement tends to focus especially on 0e and B/X-like products as the rules base, because other iterations of the rules didn't cater to this playstyle very well, which was officially "lost" (although no doubt at many tables it was still done a lot.)
This is the big contribution of 0e to me; the idea of the very slim collection of rules, a focus on tools that enable GM rulings more than exhaustive and comprehensive rules for every situation and slight change in flavor, etc. And this is what I mean when I say frequently that I'm not old-school, but I am old-fashioned. I don't like the specific rules from this era, but I do greatly prefer the playstyle inherent here. Although the motto of 3e was "Tools, not rules" in reality, 3e was full of rules, whereas it was the 0e style that gave you tools.
1e: I actually have a harder time with finding the "legacy" of this rule-system as it applies to me, as I've largely rejected the paradigm of AD&D entirely. That said, most of the really iconic content (besides some B/X stuff here and there) that we think of as D&D pertains to this version of the rules, where it first appeared and was developed. Of course, I've largely rejected that too, and play a game that while derivative of D&D isn't really meant to emulate what playing D&D specifically is like in any significant way.
But while I don't really like 1e very much and can't point to a specific thing that I'd call it's legacy in my play, at he same time, the intangible legacy is probably hard to overstate. The extent to which 1e is the expectation of what fantasy roleplaying looks like, and even the fantasy genre in general, is tremendous. Iconic adventures from 1e define D&D and fantasy overall in many ways. And even loads of basic concepts about PCs and DMing started here.
2e: 2e didn't change all that much about the rules, and most of what it did change wasn't necessarily seen as an improvement, per se. But the big story for 2e is really campaign settings much more so than rules. Now, granted, I don't use prefab campaign settings, really ever (although I'm occasionally tempted by them) but seeing them has been hugely inspirational to me, and I not only model my own settings on stuff that I see there that I like, but I borrow tons of elements from them as well.
I also like seeing stuff that is somewhat off-beat and esoteric, because it showcases exactly how far from the "baseline" that D&D can wander and yet still be very recognizably D&D. And when I want something that feels like D&D but off-kilter, modeling specifically on Dark Sun, Ravenloft or Planescape as a start is often my go-to model.
3e: 3e is the system that brought me back to D&D after many years as a wandering prodigal son. It's also the system that chased me back away from it in the end, though. But what it did was manifold: consistent, coherent rules, great settings, the OGL and all of the innovative craziness that that inspired, and ultimately, set the stage for the OSR and m20, the derivative system that I use today.
If it weren't for 3e, I wouldn't have probably come back to even quasi-traditional fantasy; I might still be wandering, if I was RPGing at all, in the worlds of modern urban fantasy or horror, or something. Or maybe I'd have become a GURPS guy. Or who knows. It wouldn't be where I am now, that's for sure.
Obviously my rules are derivative of 3e (or maybe d20, to be more specific.) Intangible influences beyond that come from many d20 sources; Eberron, Iron Kingdoms, Freeport, and more. Without d20 I wouldn't have a Sanity system in my game. I wouldn't have Action points. Neither are unique to d20, but that was the vector by which they came to me.
4e: It's curious that I've never owned 4e, never played 4e, and never even read 4e (although I did read a few sourcebooks for the fluff here and there) and while the game was not at all the kind of game that I would have wanted, it did give me a few great legacies. Some of them I was independently heading towards, but for most, I either borrowed the concept directly from descriptions of the mechanic I heard from others who played 4e, or some other such vector. Here I'm talking specifically about the concept of the minion; a capable combat opponent who nevertheless comes in large numbers and goes down with one hit, no matter what the damage, and the healing surge. The former is just fun, and while I'd arbitrarily cut back on hit points for monsters where it felt like combats were tedious grinds, I hadn't made the intuitive leap all the way towards minions. The latter, on the other hand, is super important to me, because I don't have D&D style clerical healing, so I need some kind of alternative to keep the game from being too punitive to actually model swashbuckling action.
Independently, I was also going for a clean-up and simplification of the increasingly esoteric and Byzantine and unwieldy D&D standard cosmology, even when playing D&D, so although I was gratified to see 4e do the same, I didn't need 4e for that to make its way into my games. If I ever run real D&D again, of any edition (which includes Pathfinder, for the record) I'd almost certainly houserule the alignment system to work like it does in 4e as well, assuming that I even keep alignment at all. That's another one where I was already independently going even further than 4e did anyway.
5e: Here I'd already been gone again from the D&D fold for so long that I don't even know much about how 5e works, except that it's supposed to be like 3e but without the arcane complexity that made 3e burn out so many players and DMs. That said, there is at least one concept that I'm aware of from the rules design that I've also made an element of my game, although probably not as well as it was done in 5e, honestly, and that's "bounded accuracy." I don't know why they call the concept "bounded accuracy" but it basically refers to the idea that the genre doesn't change as you level up. You don't go from playing the fantasy version of Call of Cthulhu to the fantasy version of Justice League with the same character just because you added 15 levels. Goblins are scary at 1st level (well, at least several of them together can be) but after a few levels, they're about is inconvenient as mosquitos. With bounded accuracy that doesn't happen; you level up without getting so powerful that your character's relationship with the setting fundamentally changes.
This is usually a feature of games that don't feature traditional levels, but I've decided to go with keeping levels with a truncated number of them, and that bounded accuracy's greatest nemesis is hit point escalation, so I've dramatically curbed that as well. Bounded accuracy refers specifically to having bounded bonuses on to hit, though—but the concepts are really kind of the same if you zoom up a bit.
And beyond?: I try to keep my toe in the water a bit with what's going on in D&D, although I admit to not doing it very well or very thoroughly. But the lesson here is that a great idea is a great idea, and it doesn't matter where it comes from. I don't even consider my game a D&D game, even though it's obviously specifically derivative (rules-wise, I mean) from a specific iteration of the game. If it wasn't for the OGL, though, my game would never have existed at all. Neither would other movements, like the OSR, for instance. That was still a gutsy move, and I applaud Ryan Dancey and the rest of the crew who took it.
And I might yet attempt to rework some aspects of my m20 game to more explicitly take advantage of the concept of bounded accuracy. If I do, I still probably won't do it necessarily by referring to 5e directly, though. I'll probably mine stuff like this: https://www.dandwiki.com/wiki/Understanding_Bounded_Accuracy_(5e_Guideline)