The Saya-jin Saga
This is the first saga in DBZ. It takes place five years after Goku's fight with Piccolo Diamo and his power has increased greatly since then. This saga starts off with the arrival of Raditz in a Saya-jin space ship. The first episode has Raditz meeting up with a farmer in a field. The farmer has a power level of 5 (he had a rifle which increased his power) and shot Raditz. Raditz proceeded to catch the bullet and reflect it back at the farmer, leaving him draped over the hood of his truck dead. (Pretty nifty, for all you morbid people)
Meanwhile there was a reunion at Kame House between all of the Z Warriors. Raditz arrives outside the house and announces that he is the brother of Kakarot (Goku). (This is a major part of the plot in Dragonball Z) when Raditz tells Goku for the first time that he is from the planet Vegeta and is a Saya-jin. Goku doesn't believe Raditz at first so Master Roshi tells Goku about how his adopted grandfather, Son Gohan, found a Saya-jin space ship and raised Goku as his grandson. Raditz tells everyone how Goku was sent to Earth as a baby to destroy all life on the planet. Master Roshi says that Goku was violent baby at first but fell down a ravine and hit his head. This made Goku forget all about his mission to destroy Earth and turned him in to the loving man he is.
At this Raditz grabs a hold of Gohan and Goku tries desperately to get his son back without success. Raditz tells Goku that if he puts 100 dead bodies on the beach, he can have his son back. Goku of course refuses and Raditz leaves with Gohan. Piccolo now comes to the island and faces Goku. Goku and Piccolo are still bitter enemies from their past battles but they know their only chance to win is to team up against Raditz. Since Piccolo and Goku can both sense ki, they find Raditz pretty easily since he is the most powerful being on Earth at the time. A battle rages between the three warriors and Piccolo and Goku are completely outmatched. An infuriated Gohan sees his father being tortured by Raditz and breaks out of the space pod he was being held in. Gohan's power level shoots up to 1300 and he head butts Raditz right in the chest. This doesn't do much damage but weakens Raditz's armor, making a vulnerable area for Piccolo and Goku to take advantage of. Gohan lost all of his power after the attack and Raditz knock�s him out. This attack against his son made Goku angry enough to summon the strength to grab Raditz. Goku has Raditz in a full nelson and will not let go. This gives Piccolo enough time to charge his Makankousappou. The corkscrew attack bores its way through both Raditz and Goku, killing them both. This marks the end of the first part of the Saya-jin Saga but before Raditz died he said that there were two other Saya-jin headed to Earth who are much powerful that he is. This alerts the Z Warriors and they decide to train for the fight. Gohan is taken away to train with Piccolo because Piccolo sees Gohan's true fighting potential. The others train in their own way. Goku goes to heaven and begins his journey on Snake Way. A journey that takes about 3 months. Goku reached King Kai's planet. This is where he trained and learned his most effective attacks, the Kaio Ken and Genki Dama. These attacks and training increase Goku�s power level greatly and help him a lot with other battles.
The next and more exciting part of the Saya-jin Saga is the Vegeta Saga. It can best be described as a Sub-Saga because it is not separate from the Saya-jin Saga. It has been an entire year since Raditz was killed and every one of the Z Warriors had become much, much stronger. Two Saya-jin, Vegeta and Nappa, arrive on Earth because they heard about the Dragon balls through Raditz's scouter. Now the real fighting begins with Nappa, who appears to be the stronger of the two. But with people like Krillin around, size is no indication of power. Anyway the fighting begins and Piccolo, Tienshinhan, Yamcha, and Chaozu are all killed by Nappa in one way or another. The only ones left standing are Gohan and Krillin (thanks to some Senzu beans). Goku finally arrives on earth and takes out Nappa easily, but doesn't kill him. The heartless Vegeta kills his lifelong servant, Nappa, without a second thought.
Now the real fighting begins. The long awaited battle between Vegeta and Goku kicks off with a seemingly equal match between the two. Even with his new Kaio Ken attack, Goku is beaten very badly by Vegeta. This is mainly because Vegeta transforms into his Oozaru form, making his power multiply ten times. Unlike young Goku and Gohan, Vegeta can control himself when he is in the Oozaru form. He states that he has trained in that form, which is why he even remembers the events that happen during the transformation. Vegeta now beats Goku horribly, breaking his legs under his huge boots and crushing him in the palm of his hand. This goes on until Yajarobe, can't take the screams of his friend Goku any longer cuts off Vegeta's tail with a move called the Iai Zari. ( Yajarobe is not the coward that FUNImation makes him out to be. They probably make him so afraid for comic relief)
Goku is now totally wrecked from being crushed and ground into a pulp by Oozaru Vegeta. Gohan can't take seeing his father hurt so badly and takes Vegeta on himself. He is no match for Vegeta at all. While Gohan and Vegeta are still fighting, the half-dead Goku calls over the half-dead Krillin and tells him that he has been gathering energy for the Spirit Bomb all along. Goku cannot perform the attack by himself so he gives the energy to Krillin and instructs him how to form the energy into a ball. Krillin stands high on a mountain and waits for the right time to throw the Genki Dama. He nearly throws it incorrectly until King Kai contacts Krillin telepathically and tells him the proper way to "feel out the right time." Krillin finally throws the Spirit Bomb and misses. Gohan is in the direct path of the Spirit Bomb and is incredibly frightened when Goku says that is won't hurt him unless he has evil in his heart, which he doesn't. Gohan then reflects it back and it strikes Vegeta, sending him into space and crashing back down to Earth. Surprisingly, it doesn't kill Vegeta but he is near death. Vegeta crawls on his stomach slowly back to his space ship to heal but Krillin meets up with him before he can make it there. Krillin intends to kill Vegeta with Yajarobe's sword but is stopped by the everlastingly kind-hearted Goku. Vegeta makes it back to his ship, laughs and says that he will be back to destroy Earth. Now it is up to Goku and Krillin to figure out how to wish back the others that died. Since they were already wished back with Earth's Dragon balls Goku, Gohan, and Krillin decide to go to the planet Namek to use the Namekian Dragon balls to wish them back to life. Thus leads into the Freeza Saga.