Goku
Super Saiyan: While on Namek, Frieza killed Goku's best friend Krillin. Goku's rage made him a Super Saiyan.
Super Saiyan 2:
Super Saiyan 3: When Babi-Di revived Buu, Goku knew he had to do something to stop them. He showed them SS1, then SS2 and then for the first time went SS3.

Vegeta
SS1: When training in space, a huge meteor came at him. Vegeta got hurt trying to destroy it and then started not to care. He didn't care about life or being beter than Goku. All of this rage made him transform.
SS2: The Majin power up gave him enough strength to transform to SSJ2 Level
SS3: N/A

Gohan
SS1: In the HyperBolic Time Chamber, Gohan remembered all the times he had let people down which resulted in their deaths. His rage made him transform.
SS2: During the Cell Games, Cell's Cell Jrs were hurting all his friends, Cell then killed Android 16. This added to Gohan's rage, and made him the first person to reach SS2.
SS3: N/A

Future Trunks
SS1: In his own timeline the Androids killed his best friend Gohan. His rage made him transform.
SS2: N/A
SS3: N/A

Goten
SS1: Goten surprised everyone when they discovered he could easily go Super Saiyan.
SS2: N/A
SS3: N/A

Trunks (Chibi)
SS1: Trunks also surprised everyone with his ability to go Super Saiyan with ease.
SS2: N/A
SS3: N/A