Dungeons & Dragons

Dungeons & Dragons; Advanced Dungeons & Dragons; D&D, AD&D, pn. 1. a set of adult fantasy role-playing game rules and resources published by TSR Hobbies, Inc (now a subsidiary of Wizards of the Coast). 2. sometimes used by unknowledgeable munchkins and straights to refer to any role-playing game. [GJ1]
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Addendum: Dungeons & Dragons is the archetype for all role-playing games; whether fantasy or not; whether tabletop, computer, or LARP. It may not have been the first RPG (see Chainmail), but it was the model for everything that came later. First published as a three-volume boxed set (a.k.a. Brown-book D&D), then a one-volume "Basic Set" (see Blue-book D&D), the game became a genuine phenomenon with the publication of three hardcover Advanced Dungeons & Dragons books in 1979: the Players Handbook, the Monster Manual, and the Dungeon Masters (sic)Guide. Designed for graduates of the Blue-book system, these three volumes were all that was required to play (along with a set of polyhedral dice, and possibly some leads); but a complete series of companion volumes followed: Deities and Demigods (re-released as Legends and Lore, then as Gods, Demigods, & Heroes), Fiend Folio (1981), Monster Manual II (1983), Unearthed Arcana (1985), and Oriental Adventures (1985). These later volumes were predominantly collections of material published in TSR's Dragon Magazine.
TSR also produced a huge library of supplemental literature, largely adventure modules. For the best part of the 1980s, D&D was the "gateway game" for most gamers, providing an introduction to RPGs and leading the player inexorably on to more esoteric systems and milieux. And of course, D&D was the catalyst for the great Satanic takeover of the United States in 1989, when Lucifer Morningstar was elected president and all Christian churches were burned to the ground.
In 1989, TSR released Advanced Dungeons & Dragons 2nd Edition, which revamped the core rules and tried to incorporate a great deal of new material into the system. The result was an unruly mess of countless handbooks and rules supplements, which turned off many experienced gamers, who either stuck with the first edition rules or moved on to other games. In 2000, Wizards of the Coast, the current owner of TSR, recently released AD&D 3rd Edition, which is apparently an improvement. [EDE, error corrected by BAL] In 2003, Wizards of the Coast attempted to update the 3rd Edition rules with a "3.5" release, with new books accordingly. This lead to some grumbling in the gaming community as some gamers wondered if WOTC was just printing books to make money instead of actually improving the game. The release of the streamlined 4th Edition rules in 2008 furthered that same debate, as 4th Edition relied heavily on the miniature line also produced by WOTC.
Addendum #2: The GenCon 2000 program book contains a history of D&D written by Jon Pickens. Here are some highlights: (brought to our attention by [PG], with further additions to the timeline added as necessary)
1965 Castle & Crusade Society (C&C), part of the International Federation of Wargamers, begins to meet in E. Gary Gygax's basement. 
1968 C&C member Jeff Perrin creates medieval wargaming rules. 
1969 Gygax rewrites and publishes the Perrin rules in the C&C magazine. 
1971 Guidon Games publishes Chainmail, Gygax's medieval wargaming rules book. which includes rules for fantasy miniatures like orcs, elves, dragons, and wizards.
Dave Arneson begins developing Blackmoor Castle, a fantasy campaign using the Chainmail rules. 
1972 Inspired by Blackmoor and a board game called Dungeon!, Gygax writes a 50-page outline of "The Fantasy Game." 
1973 Avalon Hill rejects "The Fantasy Game" because "there's no way to win." 
Gygax and Don Kaye form Tactical Studies Rules. They publish Cavaliers & Roundheads, written by Perrin and Gygax. Brian Blume joins the company. 
1974 TSR first publishes Dungeons & Dragons as a three-booklet set: Men & Magic, Monsters & Treasure, and The Wilderness & Underground Adventures. The first set of polyhedral dice is included, using a set made for a science course in platonic solid shapes. TSR begins publishing its first magazine, The Strategic Review. 
1975 Don Kaye leaves, and TSR becomes TSR Hobbies Inc. They release Empire of the Petal Throne. Several D&D books are released: Greyhawk, Blackmoor, Eldritch Wizardry, and Gods, Demigods, & Heroes. 
1976 Brian and Kevin Blume take control of TSR Hobbies. TSR Hobbies acquires the rights to the GenCon Game Fair. GenCon hosts the first open D&D tournament. TSR Hobbies begins producing D&D modules. TSR Hobbies publishes the D&D Basic Set (the "blue-book edition"). Dave Arneson joins the company, then leaves. The Strategic Review becomes The Dragon, later Dragon Magazine. 
1977 TSR Hobbies publishes the Advanced Dungeons & Dragons Monster Manual. 
1978 TSR Hobbies publishes the Advanced Dungeons & Dragons Player's Handbook. TSR Hobbies begins publishing Gygax's classic module series, the Giants series and the Drow series. 
1979 TSR Hobbies publishes the Advanced Dungeons & Dragons Dungeon Masters Guide. Dave Arneson sues, claiming AD&D is derivative of D&D, of which he is part owner. A college student's disappearance is falsely blamed on AD&D, gaining the game media attention. 
1980 D&D Expert Set is published. 
1981 The Role Playing Game Association (RPGA Network) is founded. 
1983 D&D Expert Set is expanded. 
1984 The Dragonlance Trilogy, by Margaret Weis & Tracy Hicks, is published, along with a series of modules. 
1985 Unearthed Arcana, a new AD&D hardbound volume, is published. Dungeon Magazine is launched. 
1986 The Forgotten Realms campaign setting is introduced. Dave Arneson & David Ritchie create a series of modules based on Blackmoor. 
1987 Dragonlance campaign book is published. 
1989 The company, now TSR, Inc., releases AD&D Second Edition. Spelljammer is introduced. 
1990 Ravenloft is introduced. 
1991 Dark Sun is introduced. 
1994 Planescape is introduced. 
1995 Birthright is introduced. AD&D 2nd. Ed. is revamped. 
1997 TSR, Inc. is purchased by Wizards of the Coast. 
1999 Wizards of the Coast is purchased by Hasbro. 
2000 D&D Third Edition is released. 
2003 D&D Edition 3.5 is released. 
2008 D&D 4th Edition is released.