SSJ: Goku becomes SSJ in the Frieza saga while fighting against Freiza. Freiza kills Krillin and this triggers Goku to becomeSSJ. USSJ: Goku goes USSJ (ultra super saiya-jin) while training in the cell saga. SSJ2: Goku becomes SSJ2 while training in the after life. SSJ3: Goku becomes SSJ3 while training in the after life. (Buu saga) SSJ4: Goku goes SSJ4 in DBGT when he sees pan crying.
Vegeta:
SSJ: Vegeta goes SSJ in the android saga. He trains under450X gravity, but he still can't go SSJ. He then gets pissed athimself and that triggers himself to go SSJ. SSJ2: Vegeta goes SSJ2 in the Buu saga MajinVegeta: This is Vegeta's version of SSJ3. He turns evil again,but Goku persuades him to become good again. SSJ4: Vegeta cheats toreach this stage. He makes Bulma create the Brute Ray, whichmakes him go SSJ4. (Vegeta skips SSJ3)
Gohan:
SSJ: Gohan goes SSJ while training in the room of spirit andtime. (Cell saga) SSJ2: Gohan goes SSJ2 In the Cell saga when Cell kills Android #16
Future Trunks:
SSJ: Trunks first goes SSJ in the Trunks Special. When Gohan dies, Trunks gets pissed and goes SSJ. USSJ: Trunks goes USSJwhile fighting Cell.
Chibi Trunks: SSJ: Trunks goes SSJ at a very young age in the Buu saga. Trunks didn't need to get pissed to go SSJ.
Goten: SSJ: Goten is the youngest person ever to go SSJ. Goten goes SSJ in the Buu saga, and like Trunks, he does not need toget pissed to go SSJ.