Kazuya climbing out of the cliff his father threw him off, as a kid. Heihachi would do the same thing when Kazuya took revenge, then one ups his son by his reaction: sending a note stating, "You should have found a steeper cliff."
Paul goes through the third tournament undefeated and defeats Ogre... Sadly, Ogre transformed after he left.
In Tekken: The Motion Picture as Heihachi gives his speech Michelle throws an axe at him. He grabs it in his teeth, bites it apart, then jumps down with no ill feelings towards her and challenges her should she make it to the final challenge.
He does much the same in Tekken 6, catching the bullet when Lars shoots him.
Asuka jumping off a building on a bike to save a kitten.
Jack-6's ending in TTT 2, reminiscent of the ending to The Iron Giant. Just as an asteroid is falling towards Earth, Jack-6 takes flight towards the asteroid and starts hammering away at it, only to have minimal effect. It looks like Jack-6 is about to fly away from it, only to fly towards it full throttle and uses all his power to break the asteroid into bits and sacrifices himself in the process.
Training mode is a staple of many fighting games, but this one goes beyond the call with an impressive and detailed list of options, up to and including specific moves for an opponent to use. Picture the likes of Jun, Jin, Heihachi, Angel, ect showing their specific signature moves and teaching you how to counter them: Badass Teacher does not even begin to describe it.
Bob's endings in Tag Tournament 2 certainly count. He dresses up as a superhero to protect innocent civilians from dangerous situations, using his SPEEED and WEIGHT!. Made even awesomer by the comic book style they're done in.
Hwoarang rescuing Jin in his Tekken 3 ending, and realizing that his power is all his own. Likewise, rejecting the Devil power in his Tekken 6 ending, realizing he doesn't need it in addition to wanting to be different from Jin.
Hwoarang's Tekken 5 ending. Broken and bleeding, he is still eager to fight Devil Jin. The music just adds to the whole scene.
The most awesome thing in Tekken history... There has been no paid character, stage or costume DLC for any Tekken game, to the point where Katsuhiro Harada outright announced that Tekken Tag Tournament 2 would have all it's upcoming DLC released for everyone completely free.
King's ending in Tekken 5. King is in a wrestling ring getting the crap kicked out of him in a tag team match, when he's able to make the tag to Marduk of all people. Marduk curbstomps them before he and King finish their opponents off with the Muscle Docking!