In an ideal world in which I had nearly-unlimited time, creative energy, funding, and access to eager and skillful players, I would probably run and/or play in a whole bunch of different D&D campaigns. You know, throw everything I think I might like at the wall and see what sticks. I thought it might be a fun exercise to figure out what kinds of campaigns I would probably enjoy using different editions or versions of D&D, since there are so many to choose from and they all differ at least slightly (and sometimes quite dramatically) in terms of both flavor and mechanics. These are campaigns in which I think I'd be almost equally happy as a DM or a player, but I'm writing about them from a DM's point of view since I'm discussing them from a design standpoint.
OD&D (Introduced in 1974) - I think a West Marches-style sandbox campaign using the Outdoor Survival board (which I actually own) would be a blast. I would start out with just the three Little Brown Books, Philotomy's Musings, The Original D&D Setting (by Wayne Rossi), and maybe a copy of Chainmail. If the players wanted me to, I could slowly introduce classes and other stuff from the various supplements and other sources over time, but at the beginning I would keep things simple. To start, classes would be limited to Fighting Men, Magic-Users, and Clerics; races would only include humans, elves, dwarves, and halflings; and Hit Dice and weapon damage would be non-variable (i.e. d6-based). Most of the world would consist of no-man's land in the wilderness, with city-states and other pockets of civilization few and far between. I'm picturing something like Mad Max or Fallout, but with swords and magic and dragons instead of guns and cars and mutants, and with primeval forests punctuated by other climates instead of just deserts everywhere. The post-apocalyptic ruins would be dungeons and fortresses, of course.
Holmes Basic (Introduced in 1977) - This is the one I'm the least certain about. This version of D&D only goes up to Level 3, so if the players want to level up past that point I would either have to switch to a different set of rules or use a fan-made expansion. Setting-wise, I'm not sure what to do with this version of D&D. My second-hand impression is that dungeon-based gameplay is described very well in the rules, while wilderness-based stuff is fairly vague. If that's the case, then a megadungeon would probably be appropriate.
AD&D 1E (Introduced in 1977) - I would run The Chaos Gods Come to Meatlandia with AD&D's craziness dial turned up to 11. You can read my review if you're curious about why I love this book so much. Go ahead, throw Unearthed Arcana and all the other "broken" stuff in there. Just go ahead and embrace the glorious mess that is early AD&D.
Okay, to be fair, I might leave out some of the annoying combat rules for the sake of speed and simplicity. The weapons-vs.-armor table and the weapons-vs.-differently-sized-enemies stuff would probably get nixed. But on the players' side of things, I would probably let them do whatever they want as long as it's allowed somewhere in the rules. I think the point of Meatlandia is that the world is getting weirder, less coherent, and more fragmented over time. A bunch of classes and subsystems that barely seem to fit into the same game would work well with that kind of setting.
This might sound like I'm bashing AD&D, but I really do like it, based on what I've seen of it and read about it. I've certainly enjoyed a lot of video games that either directly use or take inspiration from AD&D. I'm just saying that AD&D's mechanics don't always seem unified, which is not necessarily a bad thing.
Basic/Expert (Introduced in 1981) - I would try out a bunch of classic TSR modules like The Keep on the Borderlands and White Plume Mountain punctuated by Lamentations of the Flame Princess adventures to keep the players on their toes. The Keep would make a great home base for a sandbox campaign, with other adventure locations scattered around it. I wouldn't worry too much about creating a huge, coherent world right away; the world could just develop through play, starting small and getting bigger as the player characters travel.
BECMI (Introduced in 1983)/Rules Cyclopedia (Introduced in 1991) - Since these rules seem designed for running a long campaign stretching from Levels 1 to 36, with a pretty interesting "endgame," I would want to set my campaign in an expansive world with plenty of weirdness, variety, and space for exploration and conquest. I think Mystara would do the trick, especially since it includes the Hollow World. I might even throw in some time-travel shenanigans so that the players could interact with the Blackmoor stuff in Mystara's past.
AD&D 2E (Introduced in 1989) - This edition introduced a lot of cool campaign settings. I would use either Planescape, Spelljammer, Dark Sun, or some combination thereof. Enough said.
D&D 3E (Introduced in 2000)/3.5 (Introduced in 2003) - I'm actually pretty intrigued by the Eberron campaign setting, so I would probably give that a shot. I also have fond memories of a Rappan Athuk campaign (with elements borrowed from Eberron, among other things) that I played in during college, so I think I might make it a megadungeon campaign. After all, megadungeons tend to have a lot of monsters to fight, and good megadungeons tend to have a lot of interesting rooms or fight in/terrain to fight on, so D&D 3.5's highly tactical, combat-as-sport approach to battle could probably work well in such a scenario. I bet a megadungeon in Eberron would be delightfully over-the-top.
D&D 4E (Introduced in 2008)/Essentials (Introduced in 2010) - I love the video game Darkest Dungeon. Even though 4E isn't even close to being my favorite edition of D&D (although please note that I do like it, in at least some ways), I do have to admit that the combat in Darkest Dungeon reminds me very heavily of the combat in 4E, for reasons I haven't quite put my finger on. Maybe it's the emphasis on positioning and status effects, or maybe it's the way each class has a list of powers that is not too different from that of any other class, at least in terms of format and presentation. At any rate, Darkest Dungeon reminds me of a mash-up of D&D 4E and Lamentations of the Flame Princess, so maybe a 4E campaign based on the tropes and atmosphere of LotFP, video games like Darkest Dungeon and Bloodborne, and manga/anime like Berserk would be really cool. I would probably try to run the campaign in a sort of "hard mode" by setting most encounters to be balanced just slightly higher in challenge rating (or whatever 4E's equivalent is) than what the rules recommend, and then encouraging the players to choose their battles wisely. Player characters could still be badass action heroes if they're smart, but if they try to defeat every challenge head-on they'll be ground meat.
D&D 5E (Introduced in 2014) - I think I'd run A Red & Pleasant Land pretty happily with these rules. I haven't read any 5E books yet, but I'm pretty sure the author of AR&PL currently runs his campaign with this edition, and there aren't a whole lot of adventures out for 5E yet that I'm interested in, so I bet this would work well enough. Vornheim would be fair game, too.
Other ideas: I would love to run a Lamentations of the Flame Princess campaign in the "default" setting of 1600s Earth, with care taken to (mostly) adhere to James Raggi's style of play. I could probably have a lot of fun with a Carcosa campaign. Empire of the Petal Throne is very intriguing to me. I'd be excited to try out Into the Odd. I might like Ravenloft. The Underdark would probably be fun to use in almost any edition, at least on the "Advanced" side of D&D. Ghostwalk sounds neat. I would play in, but probably not DM, a Forgotten Realms campaign as long as it is sufficiently reminiscent of the Gold Box video games. Finally, I'd enjoy some cross-over action between D&D and Call of Cthulhu.