Goku
He's the main character in most of the series (after he dies for the second time, Gohan becomes the main character). He starts out as a little innocent boy, that's trained by Master Roshi. Goku was very strong for his age (he says that he's 14, but he obviously can't count), and he also has a Dragonball, I can't remember which one, that he calls it his Grandfather because, it was the only thing that he left behind, and Goku believed that it had his Grandfather's spirit.
Many episodes later, Goku grows up, and marries Chi-Chi, and has a son, Gohan. Then some more episodes later, Goku finds out that he isn't a human, but a Saiyan through his brother, Raditz. Later he finds out while he was fighting Frieza, that when he gets very angry, he turns into a SSJ (Super Saiyjin).
Chi-Chi
Chi-Chi is the wife of Goku. She first appears in the original DB series. Her main focus in DBZ, was to make her son, Gohan, become a scholar. Since Goku wants to train Gohan to become a strong warrior, there is many arguments between Goku and Chi-Chi about Gohan. Later in the series, when Gohan is in high school, Goten shows up, and she is always worries if Goten is out fighting.
Gohan
Gohan is Goku's first son, and was named after Goku's adopted Grandfather. He has tons talent and power, but he didn't realize it. Piccolo said that he was pampered too much by his parents, that's way he didn't realize his talent. So Piccolo decided to train him so Gohan could become more independent.
Goten
Goten is the second son of Goku. Unlike Gohan, Chi-Chi doesn't force him to study as much as Gohan did. At the age of 7, while training with Chi-Chi, Goten naturally became a SSJ. The only problem about that is that, Goten can never go passed SSJ level 1. Not much changes while he gets older.
Vegeta
Vegeta is one of the strong-willed characters in Dragonball Z & GT. Goku fought him, along with Nappa, to defend the lives of others. Goku makes his will become stronger. Vegeta's defeat against Goku, made him want to train and become stronger. After Goku turned into a SSJ, while fighting Frieza, Vegeta became even more jealous of him.
Vegeta's issues caused Gohan's arm to become seriously injured when Vegeta didn't have the power to attack Cell. He then accepted the things that he wasn't able to do by thanking Gohan for saving his life. Though all of his cold-hearted self, right before he gave up his life to destroy Majin Buu, he told Trunks that he loved him, and that he was sorry that he didn't pay much attention to him.
Trunks
Trunks is the son of Vegeta. He first shows up in Dragonball Z series. He's a young teen at his arrival and possesses a powerful sword, made by his mother, Bulma. Trunks explains to the Dragonball Z warriors that he's from the future, and came back to the past to heal Goku of his heart condition that he gets, and help stop the androids from destroying Earth. Later Trunks is born in the series, and after the androids were destroyed, Future Trunks returned back to the future.
Near the end of the series, he trains with Goten and his father, Vegeta. While fighting Buu, Trunks learned the fusion dance along with Goten to become Gotenks.
Bulma
Bulma appeared at the very beginning of the Dragonball series. She meet Goku and hanged around him through the series. Bulma and Goku searched for the Dragon Balls, and later in the series, it introduced her father, Dr. Briefs, the head of Capsule Corp. Bulma is his assistant manager, and they begin to create many things. Later in the Dragonball Z series, she becomes the head of her father's company.
Bulma, like Chi-Chi, adds some humor to the show, but she tends to be bossy. In the Dragonball Z series, you will see that she goes through many hair changes. Early in the Cell series, Bulma and Vegeta sleep together, and have a boy named Trunks. In the Cell series, she took care of Trunks, but in the Majin Buu series, she gives him a little more freedom.
Krillin
Krillin is Goku's best friend. He first appeared in the original Dragonball series. He along with Goku trained with Master Roshi at a very young age. He also became very good friends with Gohan.
Krillin is definitely not one of the strongest characters in the Dragonball series. What makes him a popular character is the humor that he adds, he's always seems at be in the wrong place at the wrong time. Later in the Cell series, he marries android 18 and has a daughter named Marron. He also grows hair, even though he's bald throughout most of the series.
Piccolo
Piccolo first appeared in the Dragonball series. He first appeared as an evil side of the great elder. Piccolo later met Goku in the battle tournament and showed an impressive battle, but he dropped.
When the Dragonball Z series started, he was forced to help Goku to fight Raditz. Piccolo destroyed Raditz, but also killed Goku on accident while using his special attack. After the battle, he found potential in Gohan, and decided to train him. While training Gohan, Piccolo developed a special bond with Gohan and when they fought against Vegeta and Nappa, Piccolo sacrificed his life to save Gohan.
Yamcha
Yamcha first appeared in the original Dragonball series. He was at first Bulma's boyfriend, and then became good friends with Tein and Goku. Yamcha is one of the weakest characters in the series. He fought against Vegeta and Nappa, and was killed. He went to train with King Kai, and was wished back by the Namekian Dragon Balls in the Frieza Saga.
Tein
Tein first appeared in the Dragonball series. Like Yamcha, Tein is a minor character throughout the series. He and the other Dragonball Z warriors fought against Vegeta and Nappa, but gets killed while trying to take out Nappa. He went to train with King Kai, and was wished back by the Namekian Dragon Balls in the Frieza Saga.
Later in the Cell series, he trains to take on the androids and then goes up against Cell. He gets beat up so he had to sit out.
Choazu
In the 3rd Dragonball Movie, he was the young emperor of Mifan, and in the series, he is the student of Tsuru-sennin. Choazu and Tein discover that their master was evil, and abandoned Choazu. While fighting Vegeta and Nappa, Chaozu self-destructs to take out Nappa, but sadly, Nappa survived. Later in the Frieza Saga, he was wished back by the Namekian Dragonballs.
Gogeta
Gogeta is formed when Goku and Vegeta do the fusion dance. Gogeta didn't appear much in the Dragonball series. He only appeared once and that was in the 12th movie, when Goku and Vegeta had to save Hell from being taken over by the evil Jenenba.
The first time they tried to form Gogeta, Vegeta forgot to extend one of his fingers, and they became the weak and fat Gogeta. After about 30 minutes, about how long the fusion lasts, they split into Goku and Vegeta again. Then with the help of Pikuhan, the person who stalled Jenenba, Goku and Vegeta formed into Gogeta, and easily destroyed Jenenba.
Gotenks
Gotenks is created when Trunks and Goten do the fusion dance. Gotenks formed hoping to defeat Majin Buu, but his ego got the best of him, he got dropped. Since Gotenks is formed by two Sayians, he has the ability to become SSJ.
Vegetto
Vegetto is formed when Goku and Vegeta wear one of the Fusion Earrings. The earrings are designed so that when anyone is fused, they will be combined forever instead of just the original 30 minutes. He has the highest power level of any of the fused Saiyans.
Vegetto had to fight Majin Buu, after Buu absorbed Piccolo, Gohan, and Gotenk's power. He went through spores of Buu to retrieve his friends. While Vegetto was inside of Buu, he rescued his friends including fat good Buu. When he did that, he turned Buu back to his original form and Vegetto become separated.
