Saiya-jin:
  
 Description: This is the stage a Saiya-jin is born in. Every pure-blooded Saiya-jin is born with a tail, black eyes and black hair that never changes from the day they are born. All Saiya-jin s strength varies on the amount of training they go through. All Saiya-jin s possess the unique ability to grow stronger after every battle or near death injury, where a human would generally become weaker after being fatally injured. Saiya-jins tails are their only weakness (excluding how stupid they are) but can be overcome but training. Saiya-jins are also extremely smart fighters. They love to fight, but arent that smart at much else.

 Series: Dragonball

Oozaru:

Description: User turns into a giant ape-like creature, and their power level increases 10X.  They have no control over their actions so they usually end up destroying everything within the immediate area.       

Performed by: All Saiya-jins that have ever seen a full moon (or imitation with the right kind of light) and a tail have transformed into this stage. They also all look the same excluding clothes like the Saiya-jin armor so no need for me to add a huge amount of the same looking pics.
 

Series: Dragonball

Super Saiya-jin:



Introduced by: Son Goku

Also done by: Vegeta, Trunks, Trunks (Future), Son Gohan, Son Goten, Brolly,
Goku Jr., Gogeta (Fusion), Vegitto (Fusion), Gotenks (Fusion).

Description: This level of a Saiya-jin can be the result of intense training or experiencing a great amount of rage or sadness. In order to reach this level the Saiya-jin must have a pure heart, but it can be pure good or evil. In Super Saiya-jin, the Saiya-jins hair turns blond; their eyes turn green, and their muscle mass increases. Along with these physical changes, the Saiya-jin also gets an incredible increase in speed and power. Their eyesight also is a lot better at this level. After reaching this level a first time, the Saiya-jin can reach this level again whenever they wish.

Series: Dragonball Z

Super Saiya-jin 2nd Grade (USSJ):

Introduced by: Son Goku

Also done by: Vegeta

Description: Super Saiya-jin 2nd Grade gives you a huge boost in strength over SSJ1 but makes you much slower. Think of it as SSJ1+. The Saiya-jins hair in this form also gets a little spikier.

Series: Dragonball Z

Super Saiya-jin 3rd Grade (USSJ 2): 
  
Introduced by: Trunks

Also done by: Nobody

Description: Super Saiya-jin 3rd Grade gives an even bigger amount of strength but you lose speed as well making this form useless because of how slow you become. Think of it as SSJ1++.

Series: Dragonball Z

Super Saiya-jin 2:



Introduced by: Son Gohan

Also done by: Son Goku, Vegeta, Gogeta (Fusion), Vegitto (Fusion)

Description: In this form the Saiya-jin is a little stronger than the Super Saiya-jin 3rd Grade, but doesn't have the bulky muscle mass slowing him down. There is an increase of strength over SSJ1++ but it isn't as great as from Saiya-jin to Super Saiya-jin. In order to reach this form, the Saiya-jin must be able to max out the Super Saiya-jin form and must undergo an extreme amount of rage. This level almost looks the exact same as a regular Super Saiya-jin except the hair is a more radiant shade of gold and is spikier.

Series: Dragonball Z

Mystic:
 
Introduced by: Son Gohan

Also done by: Nobody

Description: After training with the Z sword on the Kaioshin's planet, Gohan gradually grew stronger because of the Z sword's incredible weight. While testing the sword's strength on the strongest material on the planet, it broke open and the Elder Kai was released. Because the Elder Kai had permanently fused with a witch using the Potora earrings, he had the abilities to make a warrior stronger through psychic ability. In order to obtain the level of a Mystic Saiya-jin, Gohan had to stand 5 hours with Elder Kai dancing around him, and then had to sit still for 20 hours while Elder Kai psychically rearranged his power. After this ritual, the Saiya-jin's power is similar to a Super Saiya-jin 3's.

Series: Dragonball Z

Super Saiya-jin 3:

Introduced by: Son Goku

Also done by: Gotenks (Fusion)

Description: In Super Saiya-jin 3, the Saiya-jin's hair is very long and the eyebrows disappear. Though this form is very powerful, it takes a lot of ki to maintain, making it difficult for the Saiya-jin to stay in this form long.

Series: Dragonball Z

Golden Oozaru:

Introduced by: Son Goku

Also done by: Vegeta

Description: This form is like a Super Saiya-jin Oozaru. But, instead of the Saiya-jin's power increasing 10X its increased 100X from the Saiya-jin's regular power level. In order to reach this level, the Saiya-jin must have a tail and must be able to reach Super Saiya-jin.
Series: Dragonball GT

Super Saiya-jin 4:

Introduced by: Son Goku

Also done by: Vegeta, Gogeta (Fusion)

Description: In this form, red fur covers the upper body; the Saiya-jin's hair grows about shoulder length and is black, with the exception of Gogeta, who has red hair. To reach this form, you need a tail and must be able to control the Golden Oozaru form.

Series: Dragonball GT