Saiya-Jin Levels

Super Saiya Jin level 1
First seen: At Frieza Saga
First character to become a Saiya-Jin level 1: Goku(Kakarotto)
characters who can perform this: Goku(Kakarotto), Vegetta, Gotenks, Gogeta, Vegetto, Gohan, Trunks, Trunks(Chibi) Brolly and Goten

Saiya-Jin level 1 is the most simple form of a super saiya-jin. Almost all of the characters know how to perform this (except Pan, of course). Later on, this technique will be less and less effective...

Super Saiya-Jin level 2
First seen: Cell Saga
First character to become a Saiya-Jin level 2: Gohan
Characters who can perform this: Goku(Kakarotto) Vegetta and Gohan

This form was the lifesaver at the Cell saga. Gohan used this to trash Cell. And at the Buu saga, Goku and Vegitta performed this technique to complete Buu at the egg chamber. This the least used form and not even that much. Confusing with SSJ1.

Super Saiya-Jin level 3
First seen: Buu Saga
First character to become a Super Saiya-Jin 3: Goku(Kakarotto)
Characters who can perform this: Goku(Kakarotto) and Gotenks

Powerful form and consumes a lot of energy. Too bad, only 2 characters an perform this. Helped Trunks to get the dragon radar by stalling Majin-Buu.

Super Saiya-Jin level 4
First seen: Bebi saga
First character to become a Super Saiya-Jin 4: Goku(Kakarotto)
Characters who can perform this: Goku(Kakarotto), Vegetta and Gogeta

Yet very powerfull, and this form can't be learned because the Saiya-jin must have vast amount of the beam from that planet. Vegetta became a SSJ4 only because of the beam machine Bulma created for him.