Super Saiyan

Goku
Goku went to this level in the Frieza saga.After Frieza killed Krillin,Goku was enraged and went to the level of Super Saiyan.

Gohan
Gohan went to this level while training with his father,Goku in the Room of Spirit and Time.Gohan was determined to go Super Saiyan and finnaly did once Goku shot the kamehameha at him.

Vegita
Vegita went Super Saiyan when he was searching for Goku.During his search he ran into some trouble,realising he didn't care if he was stronger than Goku anymore he turned Super Saiyan.

Mirai Trunks
Trunks went to this level when he was just a young boy.Training with his friend Gohan the Androids attacked,Gohan went to face them and died. When Trunks so this he was overcome with emotion and turned into a Super Saiyan.

Goten
Goten went to this level while training with his mother Chi-Chi.Altough it doesn't say much about him going Super Saiyan it does say that he was the youngest one ever.

Trunks
Like Goten it doesn't say much about Trunks going to the Super Saiyan level but he was the 2nd youngest to ever reach this goal.

Super Saiyan 2

Goku
Goku reached this level while training in the afterlife with KingKai and with others in the Tournament,it doesn't say much about him going to this level,but he did achieve it.

Gohan
Gohan was the first to reach this level and also the youngest to do so. After Cell's foolish mistake Gohan achieved this level and destroyed Cell very easily.Also Gohan went SSJ2 very momentarily when training with Goku in the room of spirit and time

Vegita
Vegita reached this level during the years Goku was in the afterlife and not much was revealed about him reaching this level either.

Super Saiyan 3

Goku
Goku reached this level during the Buu Saga.I haven't seen how he reached it yet.

Super Saiyan 4

Goku
Goku reached this level during DBGT while fighting Vegita.This form is the only one where there hair stays the same color and it is also the one where they change the most.

Vegita
Vegita reached this level while fighting Goku in DBGT.Oddly Vegita did not reach this level on his own he had help from Bulma.