The Saiyan race were feared throughout the galaxy, their people all being skilled and rather barbaric-like warriors. All Saiyans are born with a monkey's tail, and upon gazing at the light of the full moon; transform into gigantic gorillas called Oozaru
Another notable ability about the Saiyan race is that if one were to be beaten severely, or near the point of death, and then healed back to full health, their strength would increase even more so. This is known by fan terms as a Zenkai.
At birth, a Saiyan is given a rank depending on their power level. A few days after being born they are sent in small space-pods to different planets to conquer. A baby Saiyan's rank decides what planet they are sent to, depending on how powerful that planet's inhabitants are. Once a planet has been rid of it's people, it is later used for business in terms of trading resources.
A legend is known throughout Saiyan history, that every one thousand years a Super Saiyan will rise up with a level of strength so immense that he would be one of the most powerful beings in the universe. It was always believed that somebody with royal blood would emerge as the next Super Saiyan, rather than one of a very low rank and power level.
In a non canon, filler telling of the Saiyans history as told by King Kai; Many years ago the Saiyans lived with the Tuffle race on Planet Plant, but the difference between the two species triggered a war that eventually saw the Saiyans leading to victory thanks to their Oozaru transformation, and renaming their planet after their King, Vegeta.
The Saiyans were not very advanced in terms of their technology, but struck a deal with the Arconian race to receive their expertise of machinery in exchange for their own power. This however eventually lead to their end, as the Arconians worked for the tyrant known as Frieza, who exploited the Saiyans with fear to work for him, but one day destroyed the Planet Vegeta when it’s king revolted. Canon wise the only full blooded Saiyans who survived were Prince Vegeta, Nappa, Raditz and Goku. Non canon Saiyans who survived were Turles, Broly and Paragus.
Related Threadsdo you think they will have super saiyan transformations? - last post @ Mar 9, 2011
Saiyans Playable or Not? - last post by @ Nov 14, 2008
Super Saiyan - last post by @ Mar 4, 2015