Super Saiyan 1

Goku-reaches this stage when Freeza comes back after getting hit by Goku's Spirit Bomb and kills Krillen

Vegeta-reaches this stage when he doesnt care anymore about Goku being stronger than him.

Gohan-turns SSJ1 when Goku fires a huge Kamehameha at him, Gohan then thinks of all the times he has let down his friends, he then turns SSJ1.

Trunks-reaches super saiyan when Gohan gets killed by the Android's in the future. He goes crazy and his hair flares up and his eyes turn completely blue and reaches Ssj1.

Gotenks-gets Ssj1 becuase when fusing Trunks and Goten alreald ygot to Ssj1.

Vegetto-gets to Ssj1 becuase Vegeta and oku were alrealdy Ssj1.

Super Saiyan 2

Gohan-reaches this stage when Cell and the Cell Jr's start beating the crap out of everybody. But I think when Cell crushes Android 16's head, thats what sets Gohan off.

Goku-somehow just learns to get to this stage when fighting Buu.

Vegeta-Never really reaches this stage but throughout the series his power goes past Ssj2 except his hair never changes.

Trunks-Never really reaches this stage but reaches his complete power when he goes back to the future, which is almost Ssj2.

Super Saiyan 3

Goku-had time while he was dead to reach the 3rd level of a super saiyan but they never show him training to be one. The first time he goes Ssj3 is when he was trying to stall Buu and Babidi from finding the Capsule Corp. headquarters.

Gotenks-Almost as soon as Trunks and Goten fuse they turn Ssj3 since their combined power is very powerful.

Super Saiyan 4

Goku-Will be up ASAP.

Vegeta-Will be up ASAP.

Gogeta-Since Gouk and Vegeta are both level 4 their combined strength automatically gained level 4 ability powers.