Super Saiyan-Jin
The first Super Saiyan-Jin appeared in the DragonBall Z series, there Gokou was fighting against Freeza. To transform into a Super Saiyan-Jin, the Saiyan must be able to build up lots of anger inside. The Saiyan must then let the anger increase to the desire of revenge.  This pushes the Saiyan-Jin's power level past the maximum limit. If the process is successful, the Saiyan-Jin should have gold hair which sticks up, and eyes that turn green. They also have this glow of golden light which wraps around them. The light is sort of like golden fire. As a Super Saiyan-Jin, their power, speed and agility are basically doubled. This was how Gokou killed Freeza in the DBZ series.
Advantage:
It increases the overall power of the saiyan.
Disadvantage:
Uses up energy faster than normal saiyan form.
Interesting Facts:
Gokou was the first Earth-raised Saiyan-Jin to become a Super Saiyan-Jin, and maybe the first Saiyan-Jin other than Brolly (The ancient legendary Super Saiyan-Jin).
Vegeta got jealous seeing Gokou as Super Saiyan-Jin, therefore he quickly went back to martial arts training. While Vegeta was in heavy weight training, he realized his limit and got so angry that he transformed into super saiyan.
Goten is the first ever Saiyan-Jin who has the natural ability to turn into a Super Saiyan-Jin, without pushing himself to the limit. Gohan found out this ability while he was training with Goten.  Goten actually changed into a SSJ for the first time while he was sparring with Chi Chi, his mother. 
Gohan turned into a Super Saiyan by training with his father Gokou during the battle with Cell.
Gohan's death (in the future) by Androids 18 and 16 triggered young Trunks' anger and the desire for revenge, hence transformed Trunks into Super Saiyan.
Who Can Reach This Form:
Goku, Vegita, Gohan, Trunks, Goten, and Brolly.