For the purposes of this short series of posts, I'm going to ignore settings that were never published in any form for Original or Classic D&D. This means that things like the Forgotten Realms and Dragonlance, which grew out of AD&D 1st edition, and later settings like Eberron and Golarion, for the D&D 3rd edition and Pathfinder RPGs will not be covered. A quick google search will turn up tons of info on those realms if you are interested.
I'll start with the "official" published settings from TSR. There's essentially 3 of them only 2 if you shoehorn Blackmoor into Mystara as TSR did, but counting Mystara's subsettings we have:
the Known World/Mystara
the Hollow World
and, almost nominally, Clark Ashton Smith's Averoigne, introduced in adventure module X2 but left to the DM to read more about to develop.
Since Hollow World and Thunder Rift are closely tied to Mystara, we'll save those three for last and start out with a quick look at Blackmoor, followed soon by the other realms. You'll also notice a setting initials icon with each entry, which we'll also use in the future to denote which setting, if any, an article post relates to.
Dave Arneson's Blackmoor
Blackmoor first saw print in OD&D supplement 2: Blackmoor with the Temple of the Frog sample adventure therein. Although there wasn't much detail about the world beyond, there's enough to pique the interest of players.
Prior to publication Blackmoor played a huge role in the development of the game itself, serving as the campaign setting for the evolving skirmish wargames Dave was running, incorporating and modifying Gygax & Perrin's Chainmail rules to form the foundation of what would become the Dungeons & Dragons game.
Unfortunately Dave's association with TSR didn't last long after the game was published and the only further material published by them for Blackmoor was the DA series of adventure modules:
DA1: Adventures in Blackmoor
DA2: Temple of the Frog
DA3: City of the Gods
DA4: The Duchy of Ten
These adventures saw Blackmoor added to the Mystara setting, far to the north of the Known World realms, but in reality, they work just fine, or even better, as a setting of their own, especially if you dig a bit and find the non-TSR Blackmoor material Dave developed later.
After parting ways with TSR, Dave coauthored Adventures in Fantasy with Richard Snider in 1979, published by Ecaliber Games, a fantasy RPG that in my opinion shares much of the theme and tone of D&D Supplement 2, but it was 1977's First Fantasy Campaign, a setting sourcebook published by Judge's Guild that really brought Blackmoor to the masses as a whole setting for the first time. If you can find a copy of this gem, there is really no better example of an old school game campaign. As a bonus, like most of JG's material, FFC is presented in a generic fantasy rule system that easily converts to D&D rules. Barring that, in 2004, Zeitgeist Games & Goodman Games brought Blackmoor back as a setting for the D&D 3e/D20 System with a beautiful hardback book that revisits and expands the setting nicely, it's a great addition to any old school library, just ignore the game system.
To me, the lure of Blackmoor is its quirky mix of sci-fi technology and fantasy. If you've enjoyed the Final Fantasy series of computer/console rpgs, you might well like the similar feel of Blackmoor. Dave was also never afraid to not take the setting too seriously, and bits of light hearted silliness actually work well to keep the setting fresh and long lived.
For further information and material on Blackmoor, check out these sites:
The official site of the late Professor Arneson. Lots of cool info and history on Dave's various gaming projects and career, including Blackmoor, and a host of links to other resources.
Havard Faanes is the undisputed master sage of Blackmoor lore online, and his blog is a great starting point and contact center for anyone wanting to learn more about the seting or about Dave's role in the origins of the D&D game. A must read.