The main characters in Dragon Ball are grouped into a team called the Z-Fighters. Currently this group consists of Goku, Vegeta, Piccolo, Tien, Chiaotzu, Yamcha, Gohan, Krillin, Goten, Trunks (both future and present), Android 18, Good Buu, Yajirobe, and in future episodes of Dragon Ball Super, Pan and Android 17. These fighters are the main parts of the Z-Fighters that are seen the most and participate in the most fights. They will occasionally get help from other characters, but mostly they will fight on their own.
Piccolo:
Piccolo was once Goku's archrival, as he was the son of King Piccolo, a villain who brought ruin to Goku's life and Earth itself. They fought several times, and he was bent on world domination, just like his father was. However, now Piccolo is one of Goku's closest and most important allies, and is an 
essential member or the Z-Fighter group. Piccolo is a Namekian, which makes him a useful asset because of his abilities. Piccolo brings strategy and stealth to the Z-fighter team, and his evil roots have been completely lost. He has help defeat or at least hold back many enemies, and he even serves as a mentor to Goku's son Gohan.
Gohan:
Gohan is Goku's oldest son, and while mostly he's been pushed aside as support on the team, there have been a few times, such as the Cell Games, where he has been put in center stage. Gohan was trained by Piccolo at first after Raditz attacked, and then his father before the Cell Games. But despite 
this training, even as an adult Gohan doesn't really lead the team, only really taking charge when Goku and Vegeta aren't there or can't fight. And now because of wanting to focus more on his own education and his eventual family, he fights less and less. However recently in Dragon Ball Super, Gohan has been getting his fighting spirit back due to the Zeno exhibition match and the upcoming universal tournament. He seems to be getting more excited for battles than he used to when he had switched to his family life. But as of now, even with Super, he seems to only take charge when he absolutely needs to, such as in Resurrection of F and when battling Super Buu.
Krillin:
Krillin is Goku's best friend and they've known each other since their childhoods. He is sort of a supporting role on the team, and isn't at all the strongest, but despite this lack of power he can still fight and have the courage to take on enemies even if he knows they're twice as strong as he is. He 
has helped Goku and the other fighters throughout the series, especially with his Kienzan (also known as the Destructo Disc) which has helped multiple times, but is less used and less helpful now. Krillin is typically made fun of by fans for being so weak and dying so many times, but he can be useful to the team if the situation is dire enough. He has also been named the strongest human in Dragon Ball, as he is stronger than Yamcha and knows how to use ki while many humans in the series do not. As of Dragon Ball Super, Krillin had retired from fighting, and had joined the police force instead. However, in recent episodes he has gotten his fighting spirit back, and now wishes to fight again.
Yamcha:
Yamcha was Goku's first fighting ally, and used to be a feared desert bandit. Yamcha, similar to Krillin is weaker than his allies, but he still offers support when he can. Earlier in the series he was more of a help 
due to both his allies and his enemies being weaker. But now he is less of a help but still keeps supporting and helping the team if he can. He hasn't been shown fighting much in recent episodes, and is now just more of a friend to the Z-fighter team.
Tien:
Another team member who used to be Goku's rival, Tien joined the team early on similar to Krillin and Yamcha. Tien is a dedicated martial artist and will often take on enemies much stronger than himself. He trains often and will try to help when he can even if he knows he can't defeat an enemy on his own. He usually serves as a distraction or diversion for strong enemies, and he has been shown to be perfectly capable of holding off an enemy until Goku or Vegeta can take over. He hates sitting on the sidelines and 
always desires to help, even if he knows it might risk his life. He is another valuable team member and friend to the other Z-fighters.
Chiaotzu:
Chiaotzu is Tien's best friend and former schoolmate. His last fight on the team was against Nappa, as Tien says that Chiaotzu "can't keep up" and now Chiaotzu simply offers moral support and friendship.
Yajirobe:
Yajirobe doesn't usually fight in Dragon Ball, however he played a large part in defeating Vegeta by cutting off his tail. He now offers a huge and important support by giving the other Z-fighters Senzu Beans from Korin.
Goku:
See the Goku page for info
Vegeta:
See the Vegeta page for info
Trunks (future):
Future Trunks is a future version of Vegeta and Bulma's son. He has appeared twice in the series through 
time travel, and both times had come to warn the other Z-fighters about the future and try to make their timeline better than his own. He helps with his knowledge of future events and by bringing future technology into the past to help with problems. With his knowledge of the future and the past and his technologies, he has proven to be a great addition to the Z-fighters when he comes along.
Trunks (present):
Trunks in the present is currently a child and is about 10 years old. He is usually only displayed as comic relief alongside Goten, but when he fuses with Goten and forms Gotenks he becomes more important and 
takes on a main fighting roll against Super Buu.
Goten:
Goten is Goku's youngest son and looks almost exactly like him. Much like Trunks, Goten mostly just serves as comic relief, and never really does much alone. He will fuse with Trunks to form Gotenks if he wants to fight.
Pan:
Pan is the daughter of Gohan and Videl, and as of Dragon Ball Super is only a baby. She plays a large roll 
in GT however, as she collects the Black Star Dragon Balls and fights on occasion. It is implied in Super that Pan will play a larger role when she grows up, as even as a baby she has a lot of power.
Android 18 (Lazuli):
Android 18 is a former villain and Krillin's wife, but is still capable of fighting. She is an android originally 
created by Dr. Gero to get revenge on Goku by killing him, but she changes her ways after the Cell Saga. She doesn't enjoy fighting as much as she used to, as she would much rather go back to protect her daughter and friends than run straight to the front lines. However, if she needs to, she will fight opponents, especially if they threaten those she cares about.
Good Buu:
Another former villain, Good Buu came about after absorbing the Grand Supreme Kai and gaining his jolly 
nature, separating himself from his evil self, Evil Buu. He befriends Mr. Satan (or Hercule) and now is a member of the team. He doesn't usually fight unless he needs to or if Mr. Satan has been threatened or hurt, and even if he is brought to fight he could just fall asleep and only Mr. Satan can wake him up and convince him to fight. Despite this he is still a valuable fighter and addition to the team.
Android 17 (Lapis):
Another former villain and Android 18's brother. He killed Dr. Gero and terrorized the Z-fighters at first, 
but after the Cell Saga he did the same as his sister and changed his ways. He hasn't been seen in awhile, but it has been shown that he now lives a calm life as a park ranger, and only officially joins the team in Dragon Ball Super when he is requested to help fight in the Tournament of Power.