(Normal) Saiya-jin:

This is the typical appearance of a saiya-jin. A normal saiya-jin has black hair, a thick, strong, muscular body, and a unique tail. Saiya-jins have the excellent natural fighting ability that causes them to consume a great amount of calories daily. In order to provide these calories, they eat a lot. Goku, a low-class saiya-jin, consumes about 10 times the appetite a normal human would eat daily. Compared to humans, saiya-jins are extremely strong. Even when hit by a Bulma's car in the beginning of the Dragonball series, Goku was not hurt. He immediately stood up after he was hit.

Saiya-jins have the super ability of changing (upgrading) to stronger forms, as described below:

Super Saiya-jin

Description: Freeza's worst fear... the Super Saiya-jin. This level is a legend early in Dragonball Z, but eventually becomes a natural form. Goku is the second person to ever reach this level, but is the first one we ever see doing it. When reaching this level the Saiya-jin's hair turns goldish blond, the eye's turn green, and his power level rises greatly. The Legendary SSJ mentioned throughout the series is Brolli. Super Saiya-jin are supposed to be ruthless killing machines, but we see that the Saiya-jin's personality barely changes after the transformation. The Super Saiya-jin level is triggered by emotional rage (usually). It can only be reached by someone with a pure heart of good or evil. Once reached the status of super saiya-jin, the Saiya-jin can go SSJ at will.

Those who achieved this form: Goku, Gohan, Vegeta, Trunks, Goten and Brolli

Ultra Super Saiya-jin

Description: This stage is between SSJ and SSJ 2. During this stage the Saiya-jin's muscles greatly increase in size. The Saiya-jin becomes very strong, but also very slow.  Attacks would do a lot of damage, but it is unlikely to hit the opponent. When Goku and his son, Gohan were training in the Room of Gravity and Time during the Cell saga, Goku demonstrated this stage to Gohan, and told him that it was useless because of it's drawback of making a saiya-jin usually slow. This stage's disadvantage is demonstrated as Trunks fights Cell and is beaten.

Those who achieved this form: Goku, Mirai Trunks, Brolli, Vegeta

Super Saiya-jin 2

Description: This stage was first reached by Gohan while fighting Evil Cell in the Cell Game. This stage is very much like the first Super Saiya-jin stage, but of course much stronger. Occasionally, the Saiya-jin who is in the form has electricity going around his body and through it. That's how you can tell the difference between SSJ and SSJ2. Also a Saiya-jin level 2 has slightly longer hair. This level is more superior than ssj level 1 in terms of strength and speed. It is also triggered by extreme rage.

Those who achieved this form: Gohan, Goku, Vegeta, Brolli

Super Saiya-jin 3

Description: Goku is the first and only person besides Gotenks to reach this stage. It is one of the strongest forms in all of Dragonball. You can tell a Saiya-jin is SSJ 3 when they have gold hair like all the other forms before it, and their hair gets really long and full. Also, the Saiya-jin's eyebrows disappear. This level is only achieved through training. After training in Heaven during the period of time after the Cell saga, Goku learned how to transform to ssj3. This form brings more power and speed, but because it uses more energy, a saiya-jin can only stay in this form for a short period of time.

Those who achieved this form: Goku and Gotenks

Description: This stage was made by TOEI Animation and was nothing to do with the original author of Dragonball, Akira Toriyama. During this stage the Saiya-jin's tail grows back. Their eyes turn yellow with a red outline around the eyes. The palm contains a hole that can absorb energy. Their back and most of their body is covered with red fur. The hair stays black, but gets long, not as long as SSJ 3. And again the Saiya-jin gets unbelievably powerful. Goku is the only real person to reach this level, but Buruma creates a device that turns Vegeta into a SSJ 4 also. This form is triggered by extreme rage, anger and sorrow.

Those who achieved this form: Goku and Vegeta

Oozaru

Description: When a Saiya-jin with a tail is exposed to pure moonlight (from any moon) he turns into a gigantic 20-foot tall, ape-like creature. The Saiya-jin's power level is increased ten times when turning Oozaru (Oozaru is the Japanese word for "Big Monkey") Saiya-jin's used this form to take over planets for Freeza. This form is possibly the most powerful form under SSJ level 3.  All saiya-jins, except Goku and Gohan were able to control themselves during this form.

Those who achieved this form: Goku, Gohan, Vegeta, and other saiyans that took over planets for Freeza

Ougon Oozaru (Golden Oozaru)

Description: This stage is much like the regular Oozaru stage except that the fur is golden not brown and it's of course much stronger. To reach this stage a Saiya-jin must have a tail and must receive more waves from the moonlight. The only ones to ever reach this stage was Goku and Bebi Vegeta during Dragonball GT. Vegeta reached it while Bebi was inside of him and attacked his friends. He was eventually defeated by Goku.

Those who achieved this form: Goku and Bedi-Vegeta.