Gouken is the brother of Akuma. He trained Ryu and Ken in Japan. Gouken and his brother Gouki (known as Akuma in the West) were disciples of Goutetsu. He was thought to have been murdered by Akuma, but according to the newest game in the Street Fighter series, he managed to survive.
Gouken was inspired by the hoax Sheng Long, the supposed master of Ryu and Ken created by the magazine Electronic Gaming Monthly (EGM) in an April Fools' prank (February 1992), Capcom created two characters: Gouken, master of Ryu and Ken and Gouki (known in the West as Akuma), brother of Gouken.
Gouken first appeared in Masaomi Kanzaki's Street Fighter II manga (1993-1994), appearing as a playable character only in Street Fighter IV.
In Street Fighter II: The Animated Movie, the master's name is Goutetsu, the name has been retonned as the name of the master of Gouken and Akuma.
The name Sheng Long was used in the comic book published by Malibu and in the game Street Fighter: The Movie, where Sheng Long is Akuma's brother.
Street Fighter II Turbo
In this series, Gouken was killed by Akuma, causing Ryu to hunt Akuma seeking vengeance for his master's death. When they finally met, Gouken appeared in a spectral form, telling Ryu that he finally passed the final test and one day Ryu would surpass him. He continued to fight his brother and the outcome of their battle is unknown.
Street Fighter IV
It is revealed that Gouken survived the battle against his brother, having emptied his soul of emotions for a frame second before being attacked by the Shun Goku Satsu; thus, he was left on a coma. After awakening years later, he leaves his dojo to find his students' whereabouts. Pleased to see them having gone so far, he however wanted to test them himself in battle and went on to sign up to the S.I.N's tournament.
After Seth was defeated, Gouken finds Ryu and manages to seal the Satsui no Hado within him. Akuma appears then and becomes furious to find out the power was sealed away. Gouken is challenged by Akuma, with Ryu as the prize. The outcome of the fight is unknown, but it's known that both survive and Ryu does not go to Akuma.
Later on, Ryu and Ken tail Gouken and request him to stay around for a while longer, but Gouken says that they are both grown men and don't need a master.
Street Fighter V
Gouken appears in Ryu's prologue, training him to control the Satsui no Hado within him. They are later met with Rashid, accompanied by his servant Azam, who challenges Ryu to a duel. Gouken gives some advice to Ryu, that accepts Rashid's challenge. After a brief fight between both, Ryu decides to leave to further understand more about his own power, as Gouken asks him to meet Ken, who is worried about Ryu.