Saiyan/Saiya-Jin Levels
For the record it's Saiyan in the US and therefore I will be refering to them as such in this section

First form(Saiyan): All Saiyans are born in this form. The hair tends to stay in one style throughout their lifetime unless forced otherwise. Most Saiyans are born with power levels from 5-500. Goku's was 2(Saiyans are rarely this weak at birth). There was a rare occasion with Brolli, whos power level was 10,000 on the day he was born.
-all Saiyans

Oozaru: This form can only be reached by true saiyans when they look at moonlight. They become a giant ape with ten times their original power level. If their tail is cut off they revert back to their original form.
-Goku
-Vegeta
-Gohan
-Most other Saiyans not in the series(Like Bardock and his team)

Super Saiyan(SSJ): After a long period of hard training a saiyan may acheive The status of SSJ. However most of the time this is triggered by a mix of a high power level and a strong surge of emotion. When a saiyan turns SSJ there hair will stick up and turn gold, they will get green or blue eyes. After a saiyan becomes SSJ there power becomes immense and is suppossidly unimaginable. This immense power though can change a saiyan's personality, but this depends on who it is.
-Goku
-Vegeta
-Future Trunks
-Trunks
-Gogeta(fusion of Goku/Vegita)
-Gohan
-Brolli
-Goten
-Gotenks(fusion of Goten/Trunks)
-Vegetto(Goku/Vegeta with the Potara earings)

USSJ(Ultra Super Saiyan): A better version of super saiyan level one. This was only reached by Vegeta in the early Cell saga when he started his battle against imperfect Cell. Body mass increases greatly causing slightly stronger than SSJ physical strength and slightly decreased agility/speed.
-Vegeta

USSJ2(Ultra Super Saiyan level 2): Another enhanced version of super saiyan level one. Only reached by Future Trunks right before the Cell Game, USSJ2 causes body mass to increase tremendously but physical strength and speed isn't much more than USSJ(Although it looks way cooler).
-Trunks
Super Saiyan level 2(SSJ2): The saiyan's hair is golden, like SSJ but it's slightly longer and doesn't stick up as much, and their body lets off sparks of energy. The saiyans power level increases by about another 20% from SSJ but their speed more than triples. This was first achieved by Gohan in his fight against Cell, by Goku in the Buu saga when he trains on King Kai's planet, and by Vegita when Bebi took over his body and made him a Majin.
-Gohan
-Future Trunks
-Goku
-Majin-Vegita
-Brolli
-Gogeta(fusion of Goku/Vegita)
-Vegetto(Goku/Vegeta with the Potara earings)
 

Super Saiyan Level 3(SSJ3): The saiyans hair becomes ankle length and doesn't stick up nearly as much as SSJ or SSJ2, eyes turn green, and causes the saiyans eyebrows to completely disappear. The Saiyans power level becomes immense compared to SSJ2, but it takes up a lot of energy to maintain so time in this form is limited.
-Goku
-Gotenks(fusion of Goten/Trunks)
-Vegeta

Super Saiyan Level 4(SSJ4): A saiyan's hair becomes black and slightly longer than original form, there body is covered in red hair, their tail grows longer, their eyes turn gold, but if this is reached from a fusion their body is covered in black hair and their normal hair turns red. Power level more than triples from SSJ3, and they can stay in this form much longer than SSJ3, but few saiyans make it to this level.
-Goku
-Vegeta
-Gogeta(fusion of Goku/Vegita)

Ultimate Super Saiyan: This form has only been achieved by Brolli in movies 8, 10 and 11. His body mass and power level increase many times more than USSJ or USSJ2, but in turn it also slows Brolli down more than USSJ or USSJ2(sounds bad, but the incredible power is well worth the loss of speed)
-Brolli
Golden Oozaru: This can only be achieved by SSJ-SSJ4 when they look at a full Earth, they become a giant ape with golden hair and their power level increases over fifteen times the power level of the super saiyan(pretty sweet deal).
-Goku
-Bebi Vegeta