Son Gokuh

Personality

Son Gokuh is the main hero in both DragonBall and DragonBall Z. He is a Saiyan, or Saiyajin, son of Bardock, brother of Radditz (who kills him in the beginning of the series) and his original task when he came to Earth, as a child, was to destroy the planet. He quickly forgot his mission, however, due to the efforts of Son Gohan, the old man who raised and named him (Gokuh's Saiyan name is Kakarot, but only Vejita calls him that). DragonBall essentially tells the story of Gokuh's childhood and his adventures after meeting Buruma and learning about the Dragon Balls.
In DragonBall Z, on the other hand, Son Gokuh is a grown man and marries ChiChi, unofficially the strongest woman in existence, at least until Videl came along. He has two sons, although one of them is born well into the series. Their names are Son Gohan (named after Gokuh's adoptive grandfather) and Son Goten, eldest and youngest, respectively.
Gokuh is basically a nice guy. He never seems to be sad or depressed and never refuses to help other people. A kind of happy-go-lucky person. Until he meets an opponent, of course. In battle, he's a great warrior and is naturally gifted in martial arts, as Vejita painfully admits.

The famous KameHameHa

Technique

Besides a certain combat instinct, Gokuh practices a lot and is the first one to reach SSJ and SSJ3 states. He has had several martial arts masters in his life and one of them, an old man called Mutenroshi, teaches him the famous KameHameHa, a devastating technique that can blow a hole through just about anything (battle opponents included). Firstly, a great amount of energy is concentrated between one's hands (Gohan actually gets to do this with just one hand, during the battle with Cell). The picture on the left shows the final phase of this move, the part where the "Ha" syllable is pronounced and the accumulated energy is released.
When Son Gokuh dies for the first time (weird thing to say, if you think about it) he meets a curious creature called Kaiou-Sama. This is one of the elements of a monarchic dynasty in the Otherworld and he gets to have his own personal, despite small, planet. Here, Gokuh learns another technique, called Genki-Dama. This allows Gokuh to concentrate energy from living beings in the vicinity (a light-years wide vicinity, if necessary) by holding up his hands, creating a huge fireball that he throws at the opponent. Its effectiveness varies. First attempts against Vejita didn't work all that well, but eventually he suffered serious damage by it (actually, it was Kuririn who launched the attack, guided by an injured Gokuh, who gave him the powers). It also failed at first against Freeza, one of the major villains, who was able to defend himself without much fuss. Yet later, while Gokuh's friends distracted the evil creature, our hero was able to concentrate a huge amount of power (it took him several episodes to do so!) and Freeza almost got killed.

After defeating Freeza, Son Gokuh ends up on a planet where its strange inhabitants teach him another very important technique. Its name is Shunkan-Idou (Teleport) and it allows Gokuh to move instantly from one place to another. He can also carry other people with him, as long as they are directly or indirectly in physical contact with him. To execute the transportation, Gokuh needs to focus on someone's energetic emissions, so this can take some time. That's probably why Gokuh seldom uses this process in actual battle.
Finally, after dying for a second time, Son Gokuh learns a special technique in the Otherworld: the fusion. Through a few not-so-elegant steps, two warriors with the same fighting capability can merge into one extremely powerful being. It only lasts half an hour, though, and the radically increased power often brings out a blinding pride that misleads the fighter.
Of all the warriors, Gokuh is without any doubt the one with the richest technical abilities and he doesn't keep them just to himself. Kuririn is given the chance to use the Genki-Dama in the fight against Vejita; both of Gokuh's sons are familiar with KameHameHa; and Trunks and Son Goten are the first to try the fusion technique.

Roles in the major battles

Battle against:	Role:	Son Gokuh in SSJ
Vejita	Vejita's target was Son Gokuh, who was resurrected in order to fight the two Saiyans that landed on Earth. Gokuh fought bravely, but was severely injured during the battle and it was Kuririn and Gohan who helped him.
Freeza	Son Gokuh was the main responsible for the defeat of Freeza. After a terrible battle of strength and intelligence, Gokuh thought he had taken care of Freeza for good, using the Genki-Dama technique. He was mistaken and Freeza killed Kuririn and injured Piccolo badly. With the anger, Gokuh reached SSJ and the final part of the battle began. Gokuh eventually won, outsmarting his opponent by leading one of Freeza's homing energetic saws into its creator.
Cell	Gokuh died fighting Cell. The initial Cell vs. Gokuh combat showed Gokuh was not powerful enough to beat Cell. Yet it allowed Gohan to observe Cell's techniques in order to defend himself later. When Gohan was about to kill Cell, this monster starts expanding like a balloon. Had he exploded, Earth would have been destroyed, so Gokuh uses the Shunkan-Idou technique to teleport Cell to Kaiou-Sama's planet, killing himself, killing Kaiou-Sama and his pets, but unfortunately not killing Cell.
Buu	In Portugal, we haven't finished watching the series, so I can't yet fill in this section, sorry.