Legend says that every 1000 years a Super Saiya-jin will arise. He will surpass all limits and have immeasurable power. Whoever achieves this level will be the most dominate being in the universe.*

 The levels of the Super Saiya-jin

Super Saiya-jin 

This surpasses the level of a normal Saiya-jin. To achieve Super Saiya-jin, you must have a still and pure heart. Anger and rage triggers a transformation that allows the body to handle more power and speed. The physical transformation includes the hair turning golden blond, and eyes turning green.

Who can transform at this level: Son Goku, Son Gohan, Trunks, Vegita, Son Goten, Gotenks

Super Saiya-jin "stage 1 and 2"(Ultra SS)

Not to be confused with Super Saiya-jin 2, this is the level "which surpasses the level of Super Saiya-jin."  When Goku trained in the room of time during the Cell saga, he discovered that he can increase his power more than a normal Super Saiya-jin (Goku actually discovered 2 powerups Super Saiya-jin stage 1, and stage 2 where stage 2 is the most powerful but the slowest one). But he realized that while this increase makes him more powerful, it also makes him slower. This is the major weakness which means that it is no good in battle.

Who can transform at this level: Son Goku, Trunks, Vegita

Super Saiya-jin 2

The level which is superior than that of Super Saiya-jin in terms of strength and speed. Son Gohan was the first to reach this level during the battle with Cell (some may argue that this first happened during his training in the room of time as seen in the anime). It is similar in definition to the Super Saiya-jin in which rage and anger triggers the transformation. The difference physically is a little increase in hair and small electric waves surrounding the body. With this increase in powers, strength and speed all increase in sync.

Who can transform at this level: Son Gohan, Son Goku, Vegita

Super Saiya-jin 3

Quite different than the other levels, Super Saiya-jin 3 can only be achieved through training. During the time when Goku trained in Hades (after the Cell saga), Goku learned how to transform to the third level of the Super Saiya-jin. It brings even more power and speed. Physically more hair and the absence of eyebrows is seen in this transformation. The biggest weakness at this level is that it uses more energy, so a Saiya-jin can only transform to this level for a short period of time.

Who can transform at this level: Son Goku, Gotenks (Goten and Trunks fused)

Super Saiya-jin 4

In Dragonball GT, this is the "true" level of the Legendary Super Saiya-jin. While Babi was causing problems on Earth, Goku was taken to Kaio-shin's planet to train with the Dai Kaio-shin. There he was able to regrow his tail, which when used with the Earth's sun reflections (like the moon reflections), enables Goku to transform into Golden Oozaru (a large Golden ape form). While this makes him more powerful it also renders him mindless as he wrecks havoc around anything. Only with self realization was Golden Oozaru Goku able to transform into Super Saiya-jin 4.  Physically the hair is black and the body is covered with ape like hair.

Who can transform at this level: Son Goku, Vegita (with a device created by Bulma)