Heihachi Mishima is the biological father of Kazuya Mishima and Lars Alexandersson and the adoptive father of Lee Chaolan. He was the head of the Mishima Zaibatsu at the start of Tekken 1, though the company was founded by his elusive father, Jinpachi Mishima. Heihachi lost control of the company after his son Kazuya tried to kill him at the end of the first Tekken game.
After Tekken 2, Heihachi gets revenge by tossing Kazuya into a volcano (which miraculously doesn't kill him). Heihachi then takes in his grandson, Jin Kazama, and trains him in the Mishima fighting style — shortly before turning on him. Heihachi betryed his grandson as part of a scheme to combine himself with Ogre's powers; however, he needed the Devil Gene that Jin possessed in order to do so.
After Tekken 4, Heihachi is assaulted by a group of Jack-4's that capture him and detonate themselves. The opening of Tekken 5 states "Heihachi Mishima is dead." But, as usual, it was not so. Luckily for him, the explosion did not kill him, but only threw him several miles. The resilient old man then makes his return in another attempt to regain control of his company.
Heihachi, of course, practices Mishima-style Fighting Karate. For more on the general Mishima style, see Part 1 of this series.
Heihachi is the most focused on counter attacks of the entire Mishima clan. He has very powerful attacks for punishing his opponents' mistakes. Whereas Kazuya uses his strong defense to find openings for his long, damaging combos, Heihachi is more focused on short, powerful strikes. He has a wide range of very useful mid attacks, but lacks the variety of good lows that Kazuya has. His signature moves include all of the previously-discussed Mishima staples, including one I haven't mentioned yet, the Hellsweep. Performed with a Shoryuken motion and a hold of the Right Kick button, it is a multi-hit, spinning sweep-kick that can be followed up with a combo. This move immediately comes to mind when I think of Heihachi, perhaps because of how awesome his was in Tekken 1: he did three rotations, while Kazuya could only do two!
Likelihood of Appearance in SFxT/TxSF
I'd say he's 100% likely to be in both games. Harada has stated that Heihachi is his favorite character. He also said that his dream match-up is Heihachi versus Akuma.
Did I mention that Heihachi's dream is to murder his whole family?