Ogre is first mentioned in Heihachi Mishima's character profile. It states that many years after Heihachi had reclaimed control of the Mishima Zaibatsu, he formed the Tekken Force, his own military group. One of the missions of the Tekken Force was to search an ancient temple located somewhere in Mexico. Soon after arriving there, Heihachi learned that his entire force had been obliterated by Ogre. Heihachi, having witnessed the power of Ogre sought to capture it in hopes of creating the ultimate life form.
According to official canon, Ogre attacked many world-renowned martial arts masters around the world. Because many characters from previous Tekken titles were not featured in Tekken 3, it is believed that their disappearance is due to being a victim of Ogre. This is supported by the fact that Ogre's fighting style is completely formed by other character's fighting styles, many of which were those who did not appear among the cast of playable characters in Tekken 3, such as Wang Jinrei, Baek Doo San, Bruce Irvin, Lee Chaolan, and Kunimitsu. It was later revealed however, that the only Tekken fighters that Ogre attacked/killed were Baek doo San (whom he did not actually kill), the original King, and Jun Kazama, the mother of Jin Kazama. It is unknown if Kunimitsu was a victim of Ogre as she has not been featured in the plot of a Tekken game since Tekken 2.
Sometime when Jin was fifteen, his mother warned him of an approaching evil (Ogre) and told him to seek refuge with his grandfather, Heihachi. Jin, wishing to protect his mother tried to defend her from Ogre, but was knocked unconscious. When Jin awoke, he found his home burned to the ground and his mother nowhere to be seen.
Jin fled to his grandfather, Heihachi, as Jun had previously instructed. Heihachi made the decision to train the boy to become a powerful fighter, giving Jin hopes of exacting revenge on Ogre. Heihachi's goal however, was to make Jin powerful enough to lure Ogre to him.
Eventually, Heihachi announced the King of Iron Fist Tournament 3 as a way to attract many powerful fighters. As planned, Ogre appeared at the tournament, but he was defeated by Paul Phoenix (Explained in Paul's Tekken 4 prologue) before Heihachi could capture it. Also, Jin, presumably having discovered Heihachi's sinister intentions for the tournament, defeated Heihachi. Unknown to them however, Ogre was not killed, and morphed into a monstrous beast by absorbing the energy of Heihachi.
Ogre's second form (known as True Ogre in subsequent games), is capable of using all of its techniques from his previous form as well as the abilities to teleport, fly, and breathe fire. True Ogre was defeated by Jin, and a white orb of light was emitted from its body as it dissolved.
Although Ogre was not present in the 4th game, he appears briefly in Heihachi's prologue. This explains that, Heihachi devised a new plan to make himself the ultimate warrior by using the genes of Ogre that were collected after the fight with Jin. But Ogre's genome could only be integrated with the "Devil Gene", which Heihachi did not possess. He knew that Jin and the resurrected Kazuya did, so he announced The King of Iron Fist Tournament 4 to lure both of them out.
Ogre appears only in the minigame, Devil Within, as a boss. The plot details events that occur during the two month period between Tekken 4 and Tekken 5. After Jin left the Hon-Maru after the final battle in The King of Iron Fist Tournament 4, he heard that his mother, Jun, was still alive at G Corporation. When Jin traveled to their labs, he found no trace of his mother, but instead discovered that G Corporation had either resurrected Ogre, or had simply discovered another Ogre. Beneath the labs were the remains of another ancient temple, where Jin battled True Ogre once again. Ogre fled to a deeper part of the ruins, and Jin followed it.
The deeper ruins are depicted as an other-worldly crystal-like labyrinth. The enemies Jin contended with were monsters and mutants, who were likely minions of Ogre or guardians of the ruins. The boss of stage four is a giant contraption that uses a large white orb to attack. After Jin destroys this, it is revealed that he unwittingly broke the seal containing Ogre.
During the game's final stage, Jin battles True Ogre once again. Once it is defeated, it reveals yet another transformation. This form had new abilities to create giant whirlwinds and crush Jin under its large body, along with all of its previously used techniques. According to the plot, Jin overcomes Ogre and is attacked by Jack robots, causing him to transform into Devil Jin.