The "proper" spelling (is closer to the origional Japanese) of Saiyan. They are from the anime Dragonball Z.
Saiyajins come from the planet Vegita, which was blown up by Freeza. They look human, but have a monkey-like tail and extraordinary strength. When they see the full moon, they turn into huge apes (think King Kong) that are generally bad to be around. They can avoid transforming by cutting off their tails.
Saiyajins are the only ones that can go Super Saiyajin.
The Saiyajins that I know of in Dragonball Z are Son Goku and Vegita. There are two half-human, half-Saiyajins: Gohan (son of Son Goku and Chi Chi) and Trunks (son of Vegita and Bulma).