Although the early incarnations of OD&D and Basic D&D (namely, the Holmes and Moldvay Basic Sets) included sample adventures and teasers for Greyhawk and Blackmoor, the Expert set (Cook edition) was the first to truly present a setting to set your adventures in. Cook's "Sample Wilderness" introduces us to the Grand Duchy of Karameikos for the first time, and includes notes on the folk, terrain and settlements of that region. That Expert rules set also included the adventure module X1: Isle of Dread, but we'll get back to that in a bit.
Prior to its publication, the Known World had existed as the home campaign world of Tom Moldvay and Lawrence Schick, and though their world map is strikingly different, many of the locales and names later included in the published Known World are instantly recognizable. Lawrence Shick recently posted some background information and early maps from that era at the Black Gate website: http://www.blackgate.com/2015/02/07/the-known-world-dd-setting-a-secret-history/#more-95547
It's a great bit of nostalgia and trivia, and it would be possible to use Lawrence's maps with some of the later material to construct an alternate Known World setting, but that's left to individual fans with the time and desire. Let's get back to the Known World as published in the Classic D&D rulebooks.
With the relaunch of the Classic D&D with Frank Mentzer's BECMI series, it was once again the Expert set that really adds material to the Known World setting, though some of the background info in the Basic Set group adventure was later adopted into the setting. The Expert set once more delves into the Grand Duchy of Karameikos, this time showcasing the town of Threshold, a moderately sized city in the mountainous wilderlands of the region. This edition of the Expert set also included the X1: Isle of Dread adventure module, more on that later.
The BECMI series of rules sets continued with the Companion rules, and while there is not a lot of text devoted to the Known World therein, the inside back cover of the player's manual includes a drastically larger map of the world around the "Known World" region, and sets the framework for the fantasy multiverse in which the Known World exists. The net set in the series, the Master's rules, continues in the same vein, presenting the entire world map, and further developing the settings multiverse of planes. Likewise, the final rules set, the Immortals rules, contains a lot more material on the multiverse and the immortals (the Known World's "gods") that inhabit it.
The information contained in either Expert set is plenty for many DMs to start a great, long lasting campaign, and the expanded Companion and Master's world maps add a lot of places to develop a home game, most of which were never detailed in later material.
After the BECMI series, the Classic D&D rules were compiled into the Rules Cyclopedia, a great book that includes an entire chapter presenting the Known World as a ready to use campaign setting, with color maps of large areas of the world and enough information for extensive campaigns in the setting.
The later, black box "Classic D&D Game" Basic sets don't contain any material relevant to the Known World setting, though their sample adventure, Zanzer Tam's Dungeon, could be placed in any setting you wish. It's actually not surprising that all of the Basic D&D rules sets include no real setting information. The Basic game is about dungeon crawling, and the world beyond isn't really dealt with until the Expert level sets.
Some of the Basic level adventure modules do touch on the world around their dungeons, and many of adventures published for the game, at all levels of play, include material expanding the Known World. I'll go down the list, with a brief mention of what material is in each adventure, so you can tell which ones would interest you as Known World resources, not just adventures.
B3 Palace of the Silver Princess (TSR9044) Look for the orange cover original version, as it includes a map and brief details on the Barony of Gulluvia, a province of the Principalities of Glantri.
B6 The Veiled Society (TSR9086) This adventure is set in the city of Specularum, capitol of the Grand Duchy of Specularum, and includes maps and details on locations in the city. Be aware that this early version of Specularum's maps differs considerably from the revised version seen in later products.
B10 Nights Dark Terror (TSR9149) This adventure explores many different locales in the Grand Duchy of Karameikos, including Threshold, Rifflian and Xitaqa, an ancient ruin.
B11 Kings Festival (TSR9260) Another adventure set in Karameikos, introducing the town of Stallanford. Note that the king referenced in the title is Halav I, a historical figure. In this adventure, Stefan Karameikos is still Grand Duke, not King. There's quite a bit of Karameikan history spread throughout this adventure, it's a great resource for that region of the setting.
B12 Queen's Harvest (TSR9261) This module continues where B11 left off, and includes more information on the Stallanford region of Karameikos, including maps.
CM1 Test of the Warlords (TSR9117) This adventure expands the Known World setting northward, into the lands of Norwold, and includes maps and information on those lands.
CM2 Deaths Ride (TSR9118) This module continues exploration of the Norwold region, with a close look at the Barony of Twolakes vale.
CM7 The Tree of Life (TSR9166) The first half of this adventure takes place in the elven realm of Alfheim, and has some information on the land's locales and personalities.
CM9 Legacy of Blood (TSR9210) An adventure set in the Republic of Darokin, including material on Darokin city and the town of Fenhold.
DA1 Adventures in Blackmoor (TSR9172)
DA2 Temple of the Frog (TSR9175)
DA3 City of the Gods (TSR9191)
DA4 The Duchy of Ten (TSR9205) This series of adventures takes the Blackmoor setting, by D&D co-creator Dave Arneson and sets it explicitly in the northern realms of the Known World. A mini-setting in and of itself, the four volumes include plenty of maps and information on the history, personages and locales in Blackmoor.
DDA1 Arena of Thyatis (TSR9284) As the title implies, this adventure explores arena fighting in the capitol city of Thyatis, and includes a lot of information on the cities locales and people.
DDA2 Legion of Thyatis (TSR9296) Continuing on the DDA1 adventure, this one includes more material on Thyatis city, and a lot of information on the Thyatian army.
DDA3 Eye of Traldar (TSR9271) Set in Karameikos, this adventure features material on the Black Eagle Barony, Fort Doom and the town of Luln.
DDA4 The Dymrak Dread (TSR9272) Another adventure in Karameikos, exploring the Dymrak forest and its surroundings.
IM2 The Wrath of Olympus (TSR9189) This extraplanar romp starts off in the Republic of Darokin, and includes maps and a portal in the Republic's broken lands region leading to Mount Olympus.
M1 Into the Maelstrom (TSR9159) Before venturing out into the planes, this adventure is set in and around Norwold, and includes maps of the coasts of Norworld and Alphatia, and the seas between them.
M2 Vengeance of Alphaks (TSR9148) Another adventure in Norwold, with more information on the history of those lands, and new color maps.
M4 Five Coins for a Kingdom (TSR9204) This module revolves around the city of Lighthall in Norworld, and includes some information on that city.
M5 Talons of Night (TSR9214) This adventure introduces the Isle of Dawn, a large region northeast of the Known World between Norworld and Alphatia, and includes details of that island and the history of Alphatia and Thyatis's efforts to conquer it.
02 Blade of Vengeance (TSR9108) An adventure set in the Canolbarth forest region of Alfheim, including maps and details of that area.
X1 The Isle of Dread (TSR9043) I mentioned this adventure while running down the Expert Rules sets because both versions of those rules included X1 as their sample adventure module. Aside from a fun "lost world" style wilderness adventure, X1 includes a nice map of the Known World, including the Sea of Dread and the Island chains to the south. To supplement that map, there is a handy directory of all the Known World's nations, with a thumbnail description of each. Tanoroa village, and the others like it on the Isle of Dread itself is well detailed also.
X3 Curse of Xanathon (TSR9056) This urban adventure is set in the city of Rhoona, in Vestland, and serves as a great source of information on that city and the realms around it.
X4 Master of the Desert Nomads (TSR9068) The desert wilderness where this adventure is set is located west of the Republic of Darokin, providing details on those lands, and the western fringe of Darokin.
X5 Temple of Death (TSR9069) Continuing the adventure in X4, this module ventures into the Black Mountains and the land of Hule, greatly expanding the Known World to the west of the X1 map.
X6 Quagmire (TSR9081) This adventure details the Wild Lands of the Serpent peninsula, the long strip of land at the southwest corner of the Known World.
X7 The War Rafts of Kron (TSR9079) The adventure in this module takes place mostly on the floor of the Sea of Dread, and details the locations found there.
X8 Drums of Fire Mountain (TSR9127) The Isle of TekiNuraRia, where this module takes place, is located in the Sea of Dread, southeast of Thyatis. The adventure details the island and its inhabitants.
X9 The Savage Coast (TSR9129) The Savage Coast is a big expansion of the Known World setting, far to the west of Hule and the Serpent peninsula.
X10 Red Arrow Black Shield (TSR9160) Combining elements of the Companion Rules War Machine mass combat system and the AD&D Battlesystem skirmish rules, this adventure pits the nations of the Known World against the Desert Nomads from X4 and X5, with details on the armies of all the nations, and some interesting maps.
X11 Saga of the Shadow Lord (TSR9165) This module introduces the realms of Wendar and Denagoth, just north of the Principalities of Glantri, with material on both regions.
X12 Skardas Mirror (TSR9188) The quest for the artifact this module is named for explores some more minor locales around Karameikos.
X13 Crown of Ancient Glory (TSR9218) The background material for this adventure offers a lot of history and current events information for Vestland, and explores some new locales in that realm.
XSolo1 Lathans Gold (TSR9082) This solo adventure expands on X1 a bit, visiting some new locales around the Sea of Dread, including a nice map of trade routes among the coasts and islands of the Known World.
Beyond the rule books and adventure modules, the Known World blossomed into a complex and detailed world setting with the release of the D&D Gazetteers, each of which explored a different nation of the setting.
GAZ1 The Grand Duchy of KarameikosGAZ2 The Emirates of Ylaruam
GAZ3 The Principalities of Glantri
GAZ4 The Kingdom of Ierendi
GAZ5 The Elves of Alfheim
GAZ6 The Dwarves of Rockhome
GAZ7 The Northern Reaches
GAZ8 The Five Shires
GAZ9 The Minrothad Guilds
GAZ10 The Orcs of Thar
GAZ11 The Republic of Darokin
GAZ12 The Golden Khan of Ethengar
GAZ13 The Shadow Elves
GAZ14 The Atruaghin Clans
The Gazetteer boxed set, Dawn of the Emperors: Thyatis and Alphatia rounds out the Gazetteer series.
There's a few more Known World related products, but I'll save them for next time, where I'll also look at the products for the AD&D 2nd edition's Mystara setting, which is the Known World updated to the new AD&D rules.