The King's Gambit has been declined at least as far back as Greco in the early 17th century. In fact, the "Oxford Companion to Chess" (OCC) claims that Polerio introduced the moves later called the Falkbeer Counter Gambit (1.e4 e5 2.f4 d5), (though H.J.R. Murray doesn't mention this specifically but does say that Polerio's manuscripts contain "all the know varieties of the King's Gambit excepting the Allgaier [1.e4 e5 2.f4 exf4 3.Nf3 g5 4.h4 g4 5.Ng5] and the Cunningham) continuing that Polerio offered all the popular openings of the day. However, if Polerio showed us the Falkbeer, after Greco gave his single example of a Falkbeer game a quarter of a century later, the opening must have fallen far from grace and been buried in time. Below is the game that possibly supressed it's use for two centuries (Greco's manuscripts were put in book form, commonly called Calabrians after Greco's title as "il Calabrese," which was the best selling chess book up until Philidor's "Analyse" a century later [which was critical of the King's Gambit overall]) :
The Falkbeer was named after the German master, Ernst Falkbeer who supposedly analyzed it and found it quite playable. However, the first example of a game played by Falkbeer himself using the moves: 1.e4 e5 2.f4 d5, was this loss against Adolf Anderssen in 1851:
. . . and only two other Falkbeer Counter-Gambits played by Falkbeer appear in any databases to which I have access. Books haven't revealed anything to me either.
Tarrasch considered the Falkbeer a refutation of the King's Gambit and, though this doesn't seem true, historically Black has scored slightly higher than White. Up until the popularity of the Falkbeer Counter-Gambit increased in the mid 19th century, the primary method for declining was 2.Bc5. This is called the Classical variation.
The Classical variation of the KGD seemed to have reached it greatest popularity, oddly enough, during the time after the Falkbeer came into existence.
We can refer back to Greco for an early example of the KGD Classical Variation:
The same year that Anderssen beat Falkbeer's counter-gambit, he beat Dufresne who played the Classical Variation:
White, in fact, has good resourses against this defense. Morphy won against it in three different blindfold games in three different exhibitions (Morphy acutally played against it in 4 blindfold games, but one was a draw which Morphy, who had a winning position, offered his opponent when the exhibition was ended prematurely due to the late hour.)
Here are Morphy's three blindfold games:
White must resist any temptation to ignore development- afterall, that's one of the hallmarks of the King's Gambit- by taking the e pawn, as that leads to a well known trap:
The "Chess Player's Magazine," 1865, gives the following introduction to a KGD Classical Variation game in which White, a very strong amateur, beat Black, a professional and one of the strongest players in the world at that time (the game notes are from the text).
The following game was courteously placed at our disposal by Mr. Hirschfeld, who played it some time ago against Mr. Harrwitz. The game is not played by the latter with his usual ability. Mr. Hirschfeld, however, deserves great credit for the skill with which he obtained the victory. We are informed by Mr. Hirschfeld that, of the four games which he played against Mr. Harrwitz, the former won three to the latter's one.
The following game is a little brilliancy from Prince Dadian, playing white against the KGD Classical Variation:
John Washington (JW) Baird [no relation to Mrs. J.W. (Edith) Baird] and David Graham (DG) Baird were chess playing brothers from New York in the latter part of the 19th century. Whether because of genetics or upbringing, both chose to decline the marvelous Russian, Mikhail Tschigorin's King's Gambit classically. DG Baird, clearly the better of the two, won his game. JW lost.
Tony (Antony Alfred Geoffrey) Guest from Bradford was the British Amateur champion in 1888 and long-time chess editor of the "Morning Post." In the following game he beat George Freeman who chose to employ the KGD Classical Variation. But Mr. Freeman had a valid excuse:
Essex v. Surrey.— Played on November 30th. Through some misunderstanding, Mr. Freeman went to the Mecca Café instead of the City of London Club, and arriving late lost forty minutes, and had to play his first twenty-four moves in the remainder of the hour.
The great Romanticist, Rudolf Spielmann played against Tarrasch's Classical declining (why Tarrasch didn't play the "refuting" Falkbeer is a mystery to me) in the game below.
When a former world champion contender plays a former women's world champion, sparks may fly. Here Nigel Short beat Zhu Chen's Classical defense:
David Pruess threw out a King's Gambit in the 2008 U.S. Championship and beat Dean Ippolito who treated it with Classical disdain:
Unexpectedly from the 2011 Russian Championship comes a surprising and hard-fought King's Gambit Classical Variation: