There are four types of source for historical games:
One of the most well-known and useful period sources on games, this book contained not only rules but artwork of several games, some of which are not found in other sources. Of particular focus is Chess, Dice, and "Tables" games.
An English scientist in the 17th century, Willughy's manuscript was hand-written and was never completed nor published until a group of historians transcribed it in 2003. While written out of period, it explicitly references several games named in period, and in some cases may be the only surviving source for their rules. Besides text, it also contains some crude hand-drawn diagrams.
An English writer and translator who originally published his work anonymously. Similar to Willughy, it contains rules for numerous games named in period, and was considered the standard English-language reference book on games of the time.
The Royal Game of Ur - Mesopotamia, 3rd Millennium BCE. Considered probably the oldest surviving board game known. Played with four-sided dice, and is a combination of chance and strategy not unlike Backgammon.
Weiqi (圍棋) - More commonly known by it's Japanese name "Go" (碁) or it's Korean name "Baduk" (바둑) Originates in China, but exactly how long ago is not known. Earliest text reference in 5th century BCE. Simple rules, but strategically complex.
Mancala - Not actually one game, but a large family of them. The origin is not known conclusively, but there are games of this family spread all over Africa, The Near East, India, and Southeast Asia. All involve picking up groups of “seeds” and distributing them in some way in small dishes or pits, which has led to the theory that it may have been symbolic of agriculture. The most common mancala game found in the US is called "Kalah."
Pachisi - A game popular in ancient India who's exact origins are not entirely clear, but could be up to 3,000 years ago. It is still played today. It is a game for four players where each must advance their pieces around the board, with the amount of movement determined randomly by throwing six or seven cowrie shells and seeing how many land with their opening face up. This game was the inspiration behind modern American board games "Parcheesi" and "Sorry!"
Nine Men’s Morris - An ancient game dated at least as far back as the Roman Empire, but very popular in Medieval England. Each player has 9 “men” (pieces) and the board starts empty. Play starts with placing pieces, then progresses to moving pieces. Players try to form horizontal or vertical lines of 3 (“mills”), which allows the removal of an opponent’s piece from the board. This game was "Solved" by a computer scientist in the 90s, but this may be merely academic as it's doubtful if a human can perform the necessary memorization.
Tafl - A family of games of Nordic and Celtic origins. All share a common trait of having unequal sides, with one side in the center having a "king" or similar singular important piece, and the other player's having usually twice as many pieces surrounding them in some arrangement. The side with the king wins by maneuvering this piece to where it can escape, either the edge of the board or to one of several designated spaces; the opposing side wins by capturing the king. There does not appear to be a single, "standard" version of these games, as both surviving equipment and fragments of rules differ or contradict each other. For example, boards vary in dimensions and markings, and evidence shows different arrangements of pieces. Hnefatafl ("neffa-taffle") is probably the most popular variant, and is mentioned in the Norse Sagas, but evidence for how it was played is only fragmentary. The best documented variant is Tablut, from the Sami people in the Sápmi region, but it was not written down until 1732, the documentation was missing a few details, and when it was translated from Latin to English, several mistakes were made, resulting in a ruleset that was unbalanced. Most published rules for Tafl games today, including Hnefatafl, were reconstructed from Tablut and refined through experimentation to make the games balanced.
Chess - Believed to have evolved from a game in 6th century India called Chaturanga. It distributed and evolved along multiple routes, both east and west, but the version popular in Europe during the Middle Ages evolved from the Persian variant called Shatranj. The pieces gradually changed names, forms and movement rules. The game became what we know today around the mid 15th century in Southern Europe. The final rules to be added were the Bishop and Queen's long-ranging movement, castling, the pawn's opening double move, and en passant capture. Of note is the popular shapes we associate with chess pieces today is a 19th century invention, called the Staunton chess set pattern.
Xiangqi - Also known as "Chinese Chess" or "Elephant Chess." It shares a common ancestor with European chess. One of it's more interesting and unique pieces is the cannon, which moves like a rook but must jump over another piece to capture.
Shogi - Also called "Japanese Chess" or "The Game of Generals." It has a common ancestor with European Chess, but also had numerous variants in Japan from the Heian period to the Edo period. It's believe the modern version of the game emerged in the 16the century. One of it's unique features is the ability to place captured pieces back onto the board, thus using the opponent's pieces against them.
Tables - Not one game but a family of them with very similar mechanics and equipment, most of which are played on a board that today we would recognized as "Backgammon." Games of this family combine random chance using dice rolls with strategy through the player's choice of which of their pieces to move. Most were two player games, but there is one for four players and one for seven. "Backgammon" itself is simply the variant of this game family that survived into the modern era, though it should be noted that both the name and rules as we known them today did not come about until some time later after the SCA's period.
Alquerque - Originally an Arabic game mentioned as early as the 10th century, it was documented in 13th century Spain. Players each control 12 "men" and attempt to capture each other's pieces by jumping over them with their own. The original rules as written lacked some important details, so modern historians have had to partially reconstruct them through experimentation.
Catch the Hare - A asymmetric variant of Alquerque found in the same 13th century Spanish source. One player controls a group of hunters who cannot jump or capture, and the other player controls singular "hare" who can remove hunters by jumping over them. The hunters win by cornering the hare to the point it can no longer make a legal move.
Fox and Geese - A further variation of Catch the Hare, but played on a cross-shaped board. In this case, one player controls geese that cannot capture, but must corner the singular fox, who can capture by jumping. The earliest reference to this game is under the reign of Edward IV in the 15th Century, and it was popular among English royalty for centuries.
Checkers - Also known as "Draughts," this game was invented in early 12th century France. It believed to have evolved from players using existing game equipment to combine aspects of several games of the period together: The 8x8 grid of a Chess board, the disc-shaped pieces of Tables, and the jumping capture mechanic of Alquerque. The pieces were called the same name as the chess piece we today call a “queen,” because back then, that chess piece moved one space diagonally. The French called them “fers” (vizier, a corruption of a Persian word) at first, then “dames,” which the French still call the game today (“jeu de dames” or "game of queens/ladies"). The crowning rule was added in the 13th century, and compulsory capturing added in the 16th century, making it the game we know today.
“Gioco dell'oca” aka “Game of the Goose” – A race game from late period Italy, documented as far back as 1480. It is a simple race game where player’s pieces advance as a result of dice roles, and landing on certain squares has additional effects such as doubling the distance moved or losing a turn. A common modern comparison is CandyLand. At its core, it is a game of pure luck.
Glückshaus aka "Game of Seven" – A gambling/drinking game where players throw two six-sided dice and place stakes on a special board according to the value thrown. The board contains spaces with numbers 2-12. The oldest known extant board for the game is dated to roughly 1475-1525. However, there is no documentation for the game's name or rules prior to 1733, and there are numerous variations throughout Europe from the 18th to the 20th century. The game “Glückshaus” was invented in 1963 by Erwin Glonnegger who made several unsourced claims about the game's history that since have been discredited.
Moksha Patam (aka Snakes and Ladders) - A simple race game originating in ancient India, possibly as far back as the 2nd century AD. Players advance their pieces via dice rolls, and landing on certain spaces either advances them farther up the board (ladders) or takes them back to earlier spaces (snakes). The game has origins in Hindu philosophy regarding destiny and moral instruction, with the ladders representing virtues and snakes representing vices. The game was imported to England in the late 19th century and was adapted for Victorian concepts of morality.
Kubb - Sometimes confusingly called "Viking Chess," this game involves throwing wooden batons at blocks to knock them over. While superficially resembling some old lawn bowling games in that it involves "throwing things at other things to knock them over," Kubb was actually invented in the 20th century.
Shut the Box - A popular pub game in England, this one involves rolling dice and flipping numbered paddles down based on the results. While there are claims that that game originated in 12th century Normandy, no evidence has ever been shown substantiating this. Most games historians dismiss this claim entirely. The oldest clear and substantiated source as of this writing is a 1893 French journal called "La Nature: Revue des sciences et de leurs applications aux arts et à l'industrie." The journal includes a recognizable drawing of the game under the chapter "Little Inventions" and refers to it by the name "Le jeu du trac."
Tablero de Jesus - A gambling game originally presented as coming from 15th century Andalusia, it was actually an elaborate hoax, complete with falsified documentation that was essentially nonsense when looked up. It was created by an unknown renaissance faire worker in the 1970s, and then accidentally imported into the SCA.
Cloven Fruit - There are varying versions of this described as a "kissing game" or similar, with some iterations verging on lewd. However, while historically citrus fruit with cloves in them were given as gifts in Medieval France because these were expensive products at the time, they were just that: nice gifts, with no implication or expectation of anything further.
Chinese Checkers - A simple strategy game for 2 to 6 players, this game is neither Chinese, nor related in any way to checkers. It was invented in 1892 in Germany as a variation of an slightly older 19th century game called "Halma."