SSJ Levels

Name: Goku
Super Saiya-jin: In the Freeza Saga, Freeza kills Krillin which angers Goku which triggers him to go Super Saiya-jin.
Super Saiya-jin 2: When he is training in the afterlife.
Super Saiya-jin 3: When he is training in the afterlife.
Super Saiya-jin 4: In DBGT in the Baby Saga, Goku gets his tail pulled out; he turns Oozaru then Ougon Oozaru (Golden Giant Monkey) form; when he sees his granddaughter(Pan) crying, it triggers him to go Super Saiya-jin 4.

Name: Vegeta
Super Saiya-jin: When he was training in the Gravity Room, he became very strong but not strong enough to become Super Saiya-jin; he gets very angry at himself which triggers him to go Super Saiya-jin.
Super Saiya-jin 2: He reaches this stage while being Majin Vegeta.
Super Saiya-jin 3: Never Did.
Super Saiya-jin 4: He cheated for this stage; Bulma made a Brute Ray which made Vegeta go Super Saiya-jin 4 therefore he cheated.

Name: Future Trunks
Super Saiya-jin: In the T.V Special "Resist Dispair!! The Ultimate Surviving Fighters... Gohan and Trunks", when Gohan dies Trunks gets mad and he becomes Super Saiya-jin.
Super Saiya-jin 2: Never Did.
Super Saiya-jin 3: Never Did.
Super Saiya-jin 4: Never Did

Name: Gohan
Super Saiya-jin: When he was training in the Spirit Room, he got enraged that he couldn't help his friends, which triggerd him to go Super Saiya-jin.
Super Saiya-jin 2: When Cell killed Android #16.
Super Saiya-jin 3: Never Did.
Super Saiya-jin 4: Never Did.

Name: Chibi-Trunks
Super Saiya-jin: While training, he did not need extreme rage to trigger his SSJ form. Vegeta was surprised by this.
Super Saiya-jin 2: Never Did
Super Saiya-jin 3: Never Did.
Super Saiya-jin 4: never Did.

Name: Goten
Super Saiya-jin: While training, like Chibi-Trunks he also did not need extreme rage to trigger his SSJ form. Gohan was surprised by this.
Super Saiya-jin 2: Never Did.
Super Saiya-jin 3: Never Did.
Super Saiya-jin 4: Never Did.