Role-playing game modules that emulate a putative "old school" often include tables of rumors that the referee can give out to the players. Rumors are a fun way to convey setting information and hints that motivate players to explore and form goals.
Where did the rumor table begin?
It wasn't part of original D&D. It was never a part of the rules themselves. Rumor tables came with modules. The first modules are from 1975 ("The Temple of the Frog" in Arneson's Blackmoor supplement to OD&D) and 1976 ("The Palace of the Vampire Queen" by third party Wee Warriors; "The Tomb of F'Cherlak" by Jaquays in Dungeoneer magazine). Early tournament scenarios used at conventions were also one of the main bases for early modules.
These earliest published dungeons didn't have rumor tables.
The earliest example of a rumor table I can think of is from the module B1, "In Search of the Unknown," by Mike Carr. It was originally produced in 1978, and was included in the D&D Basic Set by Holmes from November of 1978 until the end of 1979.
Mike Carr is a gamer of extraordinary credentials. To name just a few of his early credits, he had created the aerial board wargame Fight in the Skies (1966), which has maintained a loyal following (played at every GenCon since the very first one), and co-created the naval warship game Don't Give Up the Ship with Gygax and Arneson. He was involved in D&D before there was D&D, as part of Arneson's Blackmoor group, where he played Bishop Carr, a very early cleric. In 1976 he joined TSR and got directly involved in D&D. He edited the AD&D Monster Manual and Players Handbook (for which Gary Gygax took sole author credit). He would leave TSR in 1983.
By the time his B1 was published, there was a consensus among D&D players, clear from early zines and early rules sets, that dungeons were kinda stupid if they didn't have back-stories. Yes, players wanted a story and a setting to make it all seem more real and meaningful. Even modules that had no rumor tables were expected to provide a "background," often a text to be read aloud to the players (before such texts were boxed to specify what should be read aloud).
B1 was designed to teach the new DM how to run a dungeon game. As it says on the cover, it was
especially designed as an instructional aid for beginning Dungeon Masters and players, specifically created to enable new Dungeon Masters to initiate play with a minimum of preparation.
The first five pages are, accordingly, fundamental advice for how to use the module and things that we may now think of as basic, like how to compute and divide experience points.
Page 6 gives the background story for the dungeon. A powerful fighter and magic-user had created a secret base underground. They collected a lot of treasure as a reward for fighting a barbarian horde. Eventually they set out into the barbarian lands but they were killed. Now their underground hideout, with its rumored treasure, is available for plundering for those willing to risk the dangers within.
Then comes the first rumor table. It's actually called "Legend Table." Each PC knows a number of legends, randomly determined, about the abandoned underground lair. Importantly, the purpose of the Legend Table is explicit (pp. 6-7):
Prior to the first adventure into the stronghold, the Dungeon Master will utilize this table to impart "background knowledge" (from rumors or legends known) to the adventurers. It will be up to the players to act upon the information they "know"; the Dungeon Master will tell them that these are legends or rumors they have heard about the place, and that is all (it will be up to the players to decide upon the value or veracity of such information).
Each player would roll 1d4. A 1, 2, or 3 indicated how many rumors that player's character would know. A 4 meant zero legends known. Then specific legends or rumors would each be determined by a roll of d20 on the Legend Table. You re-roll duplicates. If your character knew no legends, the book says you have to ask other players for information. It also says that players can choose what to share of the legends known to them. This suggests that the rumors and legends were related on the side by the DM to individual players, and then players may choose to keep their own secrets.
What were the "rumors or legends" for? It says so: they impart background knowledge. They do so in digestible droplets rather than deluges of background information.
How to deliver setting knowledge, and how much background information to deliver, is a matter of preference and dispute still today. There has been a backlash against game settings that require players to digest a book's worth of information and long lists of jargon used in the setting of their adventures. Rumors get around that for a game of limited scope, which is what a dungeon adventure is: they give some flavor about the setting but they direct the players' attention to the place to be explored. In this case, it's the dungeon, prospectively the players' first dungeon experience.
The rumor table offers specific snippets of background knowledge that may be useful, or, when they are false rumors (some being so designated already in B1), misleading. The point is that players feel their characters are in a real world that has some meaning. It's a world with a society in which people exchange information, where the dungeons are dangerous places talked about in awe and wonder. Nobody knows the truth about these places for sure. There are just legends and rumors. That's all we know. Are the PCs going to discover the truth?
Rumors fed to the players are enticing. They are mysteries to solve. They invite exploration. Who doesn't like that?
About the beginning of 1980, the Holmes D&D Basic Set would no longer include B1 in the box. It was replaced by B2, "The Keep on the Borderlands," which is credited to Gary Gygax. (Evidently he wanted the income due from the inclusion of his own book in the set.) B2 rehashed a lot of the topics covered in B1, such as computing and dividing experience. It served the same instructional purpose as B1, as it says on the cover.
B2 also included a table of rumors, but it suggests that the DM should key specific rumors to individuals at the Keep visited before the dungeon adventure. This would, in theory, entice players to socialize with as many individuals in the Keep as possible, setting up a preliminary town adventure.
B2 came out at the beginning of 1980. Gygax's slightly earlier introductory module for AD&D, T1 "The Village of Hommlet" from 1979, includes a town adventure before the dungeon adventure, like the Keep in B2, but there is no rumor table in T1. This makes it pretty clear that Gygax's slightly later B2 took the idea of the rumor table for a "Basic" game from Carr's B1. It also suggests that the rumor table was initially conceived as particular to the dungeon adventure. Dungeons were entirely unseen until explored. They had little meaningful setting around them. Legends and rumors brought the dungeon to life as a setting and hinted at their contents, promising that they were worth exploring.
The first wave of "munchkins" (pre-teens and teens) who got into D&D in the late '70s and early '80s, of which I was one, were exposed from their start in RPGs to one of either two modules both containing rumor tables. AD&D modules up to that point did not have them. Rumor tables came with my young generation's first D&D product, the Basic Set (whether in Holmes' or Moldvay's edition). It was thereafter fixed in our minds as a basic component of what a "module" could or should include.
There's a good chance that some other early RPG product that I've missed contained the seed of the rumor table. If you know of one, leave a comment. Whether there were precedents or not, it's quite clear that Carr's B1 was the first major diffusion point that established the rumor table as canonical.
[Thanks to paleologos' comment, I was prompted to write an immediate follow-up post.]