This is the first form of an assended saiyan.  First achieved by Brolly then by Goku in the Frieza saga.  Later on by Vegeta, and after the Cell saga when Goten and Chibi Trunks were born they achieved it, and were the youngest to ever do so.  In the alternate future Older Gohan achieves it and so does 14 year old Mirai Trunks.  This is achieved when a saiyan gets extremely mad about something for Goku the death of his best friend Krillin, and for Brolly his anger from Gokus constant crying as a baby.  Almost every saiyan has achieved this level except for some.  For example: Pan, Bra, King Vegeta.  In a special OVA it is said that Nappa comes back as a Super Saiyan, and even Turlus from movie 3.  The characteristics are golden hair, a golden auroa, and your strenght increses dramactically, more muscle mass, and green eyes.

Achievers:Goku, Vegeta, Chibi&Mirai Trunks, Gohan, Brolly, Goten, Goku Jr., Vegeta Jr. Nappa(supp.), Turlus

This level was first achieved by Brolly in movie 8, then by Vegeta, then Trunks in the Room of Spirit and Time, then by Goku although Goku never fought in this form, because he found the flaw in it.  To acheive this level you must feel/have anger just like you must in any other level to assend.  This level is meant to be in-between a super saiyan and a super saiyan 2.  Although it was enough for Imperfect Cell form #2, it wasn't for Perfect Cell.  As future Trunks found out.  Trunks took the level even further a level of the form that he kept from his father.  Well in pure brute strength Trunks would have won, if it weren't for the fact that the speed in this level is decreased.  So this level isn't perfect, but in more ways than others it is effective, for example Brolly was an Ultra Super Saiyan and he is by far one of the most powerful villians that there is.  Characteristics include spikier hair and muscle mass increases dramatically.

Achievers: Mirai Trunks, Vegeta, Goku, Brolly

This is the second level of an assended saiyan.  First achieved by Gohan in the Cell saga when Cell killed android 16, then by Goku and Vegeta when Majin Vegeta fought Goku.  This level is also achieved when extreme anger comes over the person, only a saiyan can achieve this level obviously.  In this level the persons hair becomes even more spikier, and the eyes stay green.  When Gohan achieved this level it was enough for Perfect Cell but proved not to be enough for Ultra Perfect Cell, but the power increases greatly so Gohan was able to produce the biggest kamehameha wave ever, that beat Cell.  Then when the Buu saga came around the level was achieved by Goku and Vegeta and they had a spectacular fight at Super Saiyan level 2.  So obviously this level is very powerful and was never thought to be surpassed until Goku achieved Super Saiyan 3, but that is another level altogether.  Characteristics are longer golden hair, acational lightning over the body, and an increase in power 10 fold.

Achievers:Gohan, Goku, Vegeta

SSJ3 was first achieved by Goku in the Buu saga.  English episode #230 and Japanese episode #245.  Believed to be the last level because SSJ4 has no black hair.  Characteristics include super long gold flowing hair similar to Radditz hair.  Also no eyebrows, green eyes with brown in the middle, lightning over the body.  This level far surpasses that of a SSJ2 but the energy is very hard to handle.  Goku found that out in GT when he tried to assend to SSJ3 but couldn't.  No other saiyan has reached this level, and it symbolizes that you exceed Oozaru.

Achievers:Goku, Gotenks

SSJ4 was first achieved by Goku in the GT series, and then by Vegeta because of Bulma's invention the Brute ray.  Some skeptics believe that it isn't really a SSJ level.  Mainly, because of the black hair and the tail.  Also Akira Toriyama wasn't the author.  It was achieved when Goku was wished back to Earth by the dragonballs and went on a rampage in the Oozaru form and then he did it and assended.  Goku in this form has the body of an adult other than a child.  The characteristics include an increase in muscle mass, red/brownish fur up the torso, black hair, eyes red rimmed.  In this form the speed increases a lot and in this form Goku gets the 10 bai kamehame-ha when Pan is killed.  This form is superior to all others, and is one of my favorites.

Achievers:Goku, Vegeta

This level was first achieved by the first saiyans around the time when the planet Vegeta was divided between the Tuffels and the Saiyans.  Then in the Bardock special to take over certain planets.  Officially in the DB series Goku was the first, then Gohan, and Vegeta those were the only people to do it.  When in this form your power increases 10 fold and is the only level below SSJ3 meaning that SSJ1-2 are weaker than Oozaru.  Characteristics include growing 45ft. tall, the person turns into a Oozaru(giant ape), and the person most of the time looses all sense of control accept for Elites who can control their actions.  To become the Oozaru the person needs a tail a full moon, or the power to make an artificial moon, and to be a Saiyan.  Also this level is needed to assend into a SSJ4 and the Oozaru is in all the series.

Achievers:Goku, Vegeta, Gohan, Bardock, Fasha, Tooro, (basically all saiyans wtih tails, except Pan, Bra, Goku Jr., Vegeta Jr.,)

A level that was achieved by Goku and Bebi-Vegeta in Dragon Ball GT.  This is the most powerful form of Oozaru, actually, the most powerful of all stages that a Saiyan-jin can achieve, demonstrated by Goku in DBGT episodes 38-40, when he swatted Bebi-Vegeta all over Planet Plant(Bebi's recreation of the Tsufuru home planet).  The main physical difference with the Ougon stage, is that the fur is yellow instead of brown.  Also before Planet Vegeta was taken over by the Saiyans, it was also called "Planet Plant", of coarse before being renamed to Planet Vegeta.

Achievers:Goku, Bebi-Vegeta

This picture is a supposed SSJ level from an unknown series called DBAF.  These levels are supposed to be SSJ5 & 6.  There is no guareentee that DBAF is real, but who knows.  As you can see the picture is Goku, with flowing white/silverish hair, a white/silverish tail, and white/silverish fur on the torso, intense muscle mass, and freaky looking clothes.  You don't have to believe in this pic.  Most think it was a reject by Akira Toriyama, but I guess you would have to go to Japan to find out the real truth about it.  In the SSJ6 picture you can see that Goku still has whitish-silverish with goldish hair.  He has a blue and black gi, with bluish eyes.

Achievers(rumor):only Goku