Goku
The main character of DB,DBZ, and DBGT, Goku was orignally sent to Earth to clear it off for purchase. The memory of his mission is lost when he fell off a cliff. After that he became a loving child and courageous person. Compared to all the other characters, he has the most abilities and is in fact the strongest. He marries Chi Chi and has two sons, Gohan and Goten.
Chi-Chi
Chi Chi is the wife of Goku. She first meets Goku as a child and asks him to marry her. Thinking that marriage is a type of food, Goku agrees. Together they have two sons, Gohan and Goten. She is highly stressed and shops a lot to make up for it. Her highest hope is for Gohan to grow up and become a scholar, rather than a warrior. When Gohan does fight, however, she is proud of him but never admits it.
Goten
Second son of Goku, Goten was conceived a little before the Cell Game. Goten has amazing power for a six year old in that he can already transform into a Super Saiyajin, something that surprised and even made Gohan a little angry since it took him a long time to master it. He and Trunks are best friends, probably cause they are the only ones that can play together and not hurt each other. When Buu is resurrected, and Vegeta and Gohan fail to defeat him, Goten is the world's last hope as he trains to master the fusion technique with Trunks. In Dragonball GT, he becomes more of a lady's man, constantly worrying about dates and never focusing on training.
Gohan
The son of Goku, Gohan excelled in both fighting and studying. After the battle with Radditz, he is taken by Piccolo to train for the arrival of the other Saiyajin. His innocence changed Piccolo from a demon into a good and courageous person. Gohan's power comes from anger, basically, the angrier he is, the stronger he is. The first to transform into Super Saiyajin 2, Gohan was able to defeat Cell. After defeating Cell, he stopped training to study and attend Orange Star High School. When Buu appeared, Gohan was once again forced to battle. After Buu's defeat, Gohan started dating Videl and soon they got married. They had a daughter named Pan later on.
Videl
Daughter of Hercules, Videl is an exceptional fighter for a human. She is stronger than her father, but doesn't know that at first. When finding out that Gohan was the Great Saiyaman, she gives him an ultimatim of either joining the World Martial Arts Tournament, or she would reveal his identity. She also forces Gohan to teach her how to fly. She and Gohan eventually marry and have a daughter named Pan.
Pan
Daughter of Gohan and Videl, Pan doesn't have too much of a role in Dragon Ball Z, but is an essential character in Dragon Ball GT. She sneaks into the ship that Goku, Trunks, and Goten are supposed to travel in to search the galaxy for the black star dragonballs. Goku and Trunks enter the ship and Goten receives a call from his girlfriend, causing him not to enter the ship. Goku and Trunks see her at the controls and she hits the takeoff button, flying into space and leaving Goten behind. She never becomes a Super Saiyajin, though no female does (Toryama you sexist pig!). Whether they can or not is inconclusive. When Goku was a Golden Giant Ape, it was she that got control of his mind in order for him to become Super Saiyajin 4.
Vegeta
The proud prince of the planet with the same name, Vegeta travels to Earth after hearing Raddiz's message about the dragon balls. Being one of the most powerful fighters in the universe, Vegeta couldn't stand that a low soldier like Kakarotto, Goku, could even stand up to him. Later in the series, Vegeta actually saves Goku, and fights along side of him for the sole reason as to be the one that has the pleasure of killing him. Though always pure evil, Vegeta learns to act more human after falling in love with Bulma and having children with her.
Bulma
One of the Dragon Ball saga's most important characters, Bulma is responsible for many essential inventions, such as the Dragon Radar. Without her, many of the most important events of the storyline never would have occured, such as Gohan and Krillen traveling to Namek in search of that planet's dragon balls. Furthermore, Trunks wouldn't have been able to return to the past, or even existed, without her.
(Kid)Trunks
Son of Vegeta and Bulma, Trunks is best friends with Goku's second child, Goten. Being that he is a year older, he is a little stronger than Goten. He too was easily able to transform into a Super Saiyajin, which surprised and angered Vegeta a little, as it did Gohan with Goten. Determined to avenge his father's death, Trunks attempts to master the fusion technique and defeat Buu. In Dragonball GT, Trunks neglects training, and work, because he just sees them as too boring. However, when the black star dragonballs must be sought for, he unwillingly joins Goku in the search.
(Teen)Future Trunks
One of the most important characters in the DBZ story, he is the son of Vegeta and Bulma. Trunks comes from the future where Androids 17 and 18 have killed all the Z fighters and cause havoc and destruction all over the Earth. Trunks is trained by Gohan, who is the only warrior who survived, but four years before traveling in the time machine, Gohan is killed also. Gohan's death is what causes Trunks to become Super Saiyajin. When coming to our timeline, he easily kills Frieza and King Cold. He keeps his identity secret from everyone, except for when he tells Goku, to preserve his existence. Trunks is known to carry a sword, which killed Frieza. After saving the past he returns home and destroys the andriods and Cell.
Bra
Bra is Vegeta's and Bulma's second child. She doesn't really play much of a role in Dragonball Z or Dragon Ball GT. Except as an annoying punk in DBZ.
Piccolo
The offspring of the original Demon Piccolo, Piccolo was Goku's arch-enemy until the Saiyajin Radditz appeared on the Earth. To overcome Radditz's power, he and Goku teamed up. After killing Radditz and Goku, Piccolo took Goku's son, Gohan, in order to train him for the arrival of the other Saiyajins said to arrive one year afterwards. Gohan's innocence changed Piccolo from a demon, to a brave and noble warrior. He even loved Gohan so much that he sacrificed his life to save him. After the arrival of Cell, Piccolo re-merged with Kami and became the strongest warrior at that time. In Dragonball GT, he decides to die when the Earth explodes due to his love for his home.
Krillen
Krillen is a monk that trained with Master Roshi and Goku. He has no nose, and no hair until later in the series. Krillen is the strongest human, but is never as strong as a Saiyajin, let alone a Super Saiyajin. He marries Android 18 later in the series, and has a daughter named Marron. He plays a semi-important role in the series, as he was killed by Freiza causing Goku to become a Super Saiyajin for the first time.
Android 18
Android 18 is unwillingly absorbed by Cell but spit out when Super Saiyajin 2 Gohan punches him hard in the stomach. Krillen is in love with her and wishes for the self-destruct bomb within her to be removed. They eventually marry and have a daugter named Marron. Android 18 is originally human but is given enhancements that make her into an android. In Trunks' future timeline, she and Android 17 are responsible for the death of the Z fighters and most of humanity.
Tien
The bodyguard of Chaozu, Tien plays a minor role, but an important one, in the three Dragonball series. He begins as Goku's enemy, which all characters did, and was the prize student of the crane master. After seeing his master for the evil man that he was, Tien leaves the crane school and joins with Muten Roshi. Tien's greatest attacks, and those that have helped out the Z Fighter, are the Multiform technique and Tribeam attack. He was also the first to perform the multiform technique.
Chaozu
The weakest energy controlling Z fighter, by far. He is left behind from the Cell fight because of this. However, his telepathic powers are fantastic, but that still doesn't help someone win a fight. In the original Dragonball, Chaozu was an emperor. Throughout all of Z and GT, he follows Tien around treating him like his brother.
Yamcha
Originally a bandit, Yamcha, with the help of his friend Puar, would rob anyone that passed through his home. When meeting Goku and the others, he decided to join them in their search for the dragonballs to make a wish of his own. At first, Yamcha was very afraid of Bulma, and all girls in general. He eventually lost that flaw and was with Bulma for awhile. Yamcha stopped training after the androids but still is a very exceptional fighter.
Hercules
Though very annoying, he is one of the most crucial characters in DBZ. Without his presence, the entire universe would have been destroyed. His influence over the people of the Earth game Goku the amount of energy needed to complete the Spirit Bomb and kill Kid Buu. He is also the father of Videl who is the future wife of Gohan. Also, without his assistance Gohan whould have never reached SSJ2.