Name: Goku.

Super Saiya-jin 1: In the Frieza Saga, Frieza kills Krillin and badly injures Piccolo which angers Goku which triggers him to go Super Saiya-jin.

Super Saiya-jin 2: When he is training in the next dimension.

Super Saiya-jin 3: When he is training in the next dimension.

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 1: 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: Was skipped, Vegeta went from SSJ2 to SSJ4, He cheated to reach SSJ4 (See the rest below).

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: Did not reach.

Super Saiya-jin 3: Did not reach.

Super Saiya-jin 4: Did not reach.

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: Did not reach.

Super Saiya-jin 4: Did not reach.

Name: Chibi-Trunks.

Super Saiya-jin 1: While training, he did not need extreme rage to trigger his SSJ form. Vegeta was surprised by this.

Super Saiya-jin 2: Did not reach.

Super Saiya-jin 3: Did not reach.

Super Saiya-jin 4: Did not reach.

Name: Goten.

Super Saiya-jin 1: 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: Did not reach.

Super Saiya-jin 3: Did not reach.

Super Saiya-jin 4: Did not reach.