Super Saiya-jin Level 1

This surpasses the level of a normal Saiyan. To achieve Super Saiyan, you must have a pure heart. What makes this possible is you have to have anger and rage triggers a transformation that allows the body to handle this humongous strength and speed.
Physical Description: Hair turns golden blond, and eyes turning green.
Who achieves this level: Goku, Gohan, Trunks, Vegeta, Goten, Gotenks, Brolli from movie8
Super Saiya-jin Ultra

Remember this is not ssj2, this is the level "which surpasses the level of Super Saiyan." When Goku trained in the room of spirit and time during the Cell saga, he figured out that he can increase his power tremendously more than the normal ssj. But he soon found out that when hes in this form the strength makes him stronger but the speed makes him slower. This is the only weakness in this transformation which means that this level is totally useless during battle.
Physical Description: Increase in muscles but slower in speed.
Who achieves this level: Goku, Trunks, Vegeta
Super Saiya-jin Level 2

This level is which is superior than that of Super Saiyan especially in strength and speed. Gohan was the first to reach this level during the battle with Cell. This is also achieved with anger and rage which immediately triggers the transformation.
Physical Description: is a little increase in hair and small electric waves surrounding the body. strength and speed all increase tremendously.
Who achives this level: Gohan, Goku, Vegeta, Gotenks, and Brolly
Super Saiya-jin Level 3

Super Saiyan 3 can only be achieved through hard training. During the time when Goku trained in kaio-samas (King-kai) place after the cell saga, Goku learned how to transform into the third level of a Super Saiyan. This level increases even more power and speed.
Physical Description: Longer hair and has no eyebrows(only in this level). The biggest weakness in this level is that it uses more energy, so a Saiyan must get the job done quickly.
Who achieves this level: Goku, Gotenks
Super Saiya-jin Level 4

This transformation is only achieved in Dragonball GT, this is a true level of a sayain this level is achieved by rage, anger, and sorrow all of this things trigger this transformation.
Physical Description: The hair is black and the body is covered with red fur. This increases the muscles, speed and strength.
Who achieves this level: Goku, vegeta
____________________________________________________________________________________

Super Saiyan is a very important word to many people out there who love saiyans! The first super saiyan was achieved by someone who went ape form, they weren't able to control it and ended up destroying himself! Vegeta expected to be able to go super saiyan first, but found he wasn't the next super saiyan, it was Goku!
There are 4 types of "super saiyan", each getting stronger and stronger.
Super Saiyan 1 - fulfilled when power level reaches a high limit, or when rage occurs over the death of a loved one. When this occurs, the saiyans hair turns yellow, spikes up, and their eye's turn green. The saiyan must be pure evil, or pure good.
Ultra Super Saiyan - It's the next step up for super saiyan 1! Trunks achieved this level, it made him muscular and strong, but it slowed him down! Goku also achieved this level but he realized the flaw. They decided not to try this again. Brolli I am thinking... was the only one able to control this stage of power... making him nearly indestructible.
Super Saiyan 2 (sienen) - fulfilled when power level reaches a high limit, or when rage occurs over the death of a loved one. This stage is much more stronger than super saiyan 1. The saiyans hair is still yellow, but grows a few more strands and is pointed up more than Super saiyan 1. Gohan was the first to fulfill this level of super saiyan.
Super Saiyan 3 - This is the next most powerful stage in dragon ball Gt. Only Goku and Gotenks were able to achieve this level of super saiyan! The saiyans hair is pointed down, and grows a few more feet!! This stage is truly powerful in my opinion!
Super Saiyan 4 - This is the most power stage of saiyans. (besides oozaru) The saiyan gets their tail back, and doesn't have yellow hair at all on their body.! Their bodies are covered with red fur, besides the chest, and they get dark red lines under their eyes. They almost look evil, but are actually fighting evil! Goku and Vegeta were the only saiyans to achieve Super Saiyan level 4! After Vegeta and Goku went this stage, the series and episodes basically end! Gogeta, the fusion of Goku and Vegeta, was also able to achieve this level, but had red hair on his head.
Goku : Realized in time chamber that there was a weakness to this stage of SSJ almost idmedily
Trunks : Learned to control it yet later found out fighting Cell there was a weakness to this stage (Cell told him)
Vegeta :Fought Cell and knew he was more powerful than Cell yet could not understand why he couldn't hit him,then he relised why and lowerd his power level (he never did it again)
Gohan :Something about him walking around as a SSJ and someone wanted to fight,he got mad when they hurt Vidle.(in movie)
Brolli :The only one that ultra SSJ did not slow down
Pan :I heard that she got ultra SSJ but since she is only 1/4 saiyan she was very weak (in movie)