Dungeons and Dragons is fantasy role-playing game first designed by Gary Gygax and David Arneson in the early 1970s. It was published by Gygax's company TSR. Dungeons and Dragons (which evolved from the Chainmail system of wargaming rules) was one of the first roleplaying games and was by far the most well-known and best selling. It was massively influential over its imitators and successors, in many ways defining what an RPG was and to some extent still is.
D&D has gone through several revisions. The first edition featured just a few character classes and monsters. Advanced D&D was published in the early 1980's, and greatly expanded the character classes, monsters and spells. During the late 1980's AD&D 2nd Edition was published, which revised the rules again, consolidating the character classes, and revising the combat system somewhat.
In 2000, a third revision, simply called Dungeons and Dragons, was published. It is based on the d20 system. It rationalizes movement and combat (especially ranged combat), removes lots of arbitrary restrictions (now you can have a half-orc monk), and incorporates skills and feats to allow players to customize their characters.
A movie, Dungeons and Dragons, based on the gaming conventions, was released in 2000.