All throughout DBZ-GT, SSJ mode is something people see and they love how the Saiya-jin often entertain by making their hair turn gold, well this section is dedicated to finding more behind the power of SSJ.
This is a transformed state in which a Saiya-jin reaches due to certain characteristics. The Saiya-jin experiences huge power surge. In this stage more Ki is transported in the Saiya-jin's body that his normal state couldn't control. Speed, Strength, and all other attributes all experience a huge increase.
This is a stage that a Saiya-jin reaches after a lost battle. They get a power increases and all attributes increase as well.
The level that Son Goku reached in Movie 4. This stage is not a "real" SSJ stage but it means the Saiya-jin's rage and other attributes are "within" the requirements but he doesn't have enough power.
The very first stage of "SSJ". This was supposed to be the original SSJ stage but as time went by more was added. Son Goku was the first this stage during the furiza saga. When Goku first used this transformation it looked like his power increased by 15 times normal, but as time progressed the power surge wasn't as great. Goku reached the level first then Mirai Trunks showed up.
There are two forms of Ultra Saiya-jin, the first form is a form used by Vegeta. While in this form he could power up passed a normal Super Saiya-jin and his muscles will increase and speed will slightly decrease but not that much. But the level trunks reached was a level that he could power up his muscles up to 4 times normal and speed will greatly decrease. The two of them achieved this level while training in the Room of Spirit and Time.
This was the stage Gohan first reached to defeat Cell. Gohan had the power inside he just didn't know how to release it, but when it came out he shocked everyone! Well this stage is pretty much Gohan's stage to me.
"The level beyond the level beyond SSJ" as Goku calls it, I see this stage as Son Goku's stage because he's the only non-fused Saiya-jin to reach this level. In this form time flies faster for the warrior that uses it.
This is said to be the legendary form. It was achieved first by Son Goku in DBGT. He achieved this form through sorrow; which appears to be why people achieve this level. Vegeta achieved it through a brute ray gun Buruma invented.