#1 Brolly, he was born on the Saiya-jin home world with Goku. Their cribs were placed next to each other. While Brolly was born with a power level of 10,000 and Goku had a meager power level of 2. When they were babies Goku managed to make Brolly sad and cry with Goku's persistent whining that wouldn't stop. This is what drove Brolly's anger towards Goku, Goten, any other DBZ warrior and his love of being evil. Please stop reading here if you do not want to further spoil the storyline/endings of movies 8,10, and 11.
While Brolly was a baby, King Vegeta learned of this child of Paragus that was born with amazing power for a child. King Vegeta had both Paragus and Brolly "thrown away" like trash. When Frieza destroyed the planet, Brolly used his amazing power to protect both himself and Paragus from the destruction.
During Brolly's childhood Brolly became increasingly difficult to control, Brolly's power was greater than ever imagined. Paragus had a scientist from a world he conquered create a devise to control Brolly, similar to a remote control of sorts. When Paragus essentially had this great power at his control, he created a "New Planet Vegeta" in an attempt to draw the Saiyan Prince (Vegeta) to the new world where Paragus would have his revenge on King Vegeta by killing his son Vegeta by either the comet that was heading towards the new planet or by Brolly himself. The plan did not work completely as planned and Paragus told Vegeta of the Legendary Super Saiya-jin who was near the new world that was destroying entire galaxies. This is what made Vegeta go to the new world.
The rest of Paragus's plan seemed to be working accordingly, but the arrival of Goku at the new world shortly after Vegeta caused problems. Seeing Goku, drove Brolly's anger and eventually Brolly could not be controlled by Paragus 's device and his plan was revealed to the Saiya-jins. Paragus tried to escape from the planet before it's eminent destruction but Brolly destroyed his space pod, with Paragus in it, killing him.
Through a very long and rigorous fight, Goku did finally defeat Brolly in movie 8 with the help of the others (Piccolo, Gohan, Trunks, and Vegeta). Brolly returns in Movie 10, somehow he survived Goku's deathblow and managed to get to another space pod, this space pod lands on earth. There is another battle, Goten and Gohan use a large Kame-hame-ha to defeat Brolly. At first there is no effect but Goku's spirit falls from the clouds and gives them emotional support as well as joining in on the Kame-hame-ha which does destroy Brolly. Finally he returns one last time in movie 11, he is cloned and is once again destroyed by Chibi (young non-future) Trunks and Goten.
#2 Brolly only appeared in three DBZ movies, #8, #10, and #11. That is why you can not find him in any DBZ time lines or saga summaries. The most important thing to know is that Brolly is the Legendary Super Saiyan. At times Goku was thought to be the Legendary Super Saiyan, but Brolly is the true one. When Brolly was a baby he was annoyed by a baby in the next crib. Brolly could never get any sleep, this eventually drove him mad. The baby happened to be Kakarot, later known as Goku. King Vegeta noticed that Brolly was stronger than himself, so he ordered Brolly's father, Paraga, to kill him. Because of Paraga was loyal to his king he stabbed his own son hoping it would kill him. Surprisingly this did not kill Brolly. When Planet Vegeta was blown up by Vegeta, Brolly made a protective bubble around him and his father, then flew them to safety. Paraga feared for his life, so he put these arm bracelet things to restrict Brolly's power. This let Paraga control his son as well as Brolly's anger so he would not destroying himself. If you remember the first Legendary Super Saiyan was killed by his own power. One day Brolly to the Earth. Brolly and Vegeta met and they realized that they were both Saiyans, but nether took much interest. Then Brolly saw Goku, the memory of the baby that kept him awake for so long came to him in an instant. Brolly became infuriated that he was in the presence of Goku, the person that drove him insane. In the first Brolly movie he was fought by Goku and the other Z fighters. In the second movie Brolly was killed, and in the third Brolly was brought back to life by the Z fighters for some reason and there was of course more fighting until [Bio-] Brolly was killed again