saiyans:

Saiyans are a species from the planet Vegeta (yes that means Vegeta was a prince). The Saiyans were very brutal and uncivilized. They killed off their counterparts on their planet (the Tuffels). They then built a rocket ship and went to another planet that had money and technology which they traded for another planet. So therefore the Saiyans became like planet brokers. They have natural abilities and desires to fight. Their tails that make them unique also give them the ability to go oozaru (ape creatures from the Saiyans when Saiyans see full moons). They can be stopped by cutting off their tails (just like what happened to Goku). They can also go Super Saiyan. This is a special status that is trigged with *extreme* anger.

Super Saiyan Level 1

Obviously, the higher the level of a Super Saiyan, the more powerful. Being so, Super Saiyan Level 1 is relatively weak (when compared to Super Saiyan Level 4.

How can you tell one has just transformed into a Super Saiyan Level 1?

First, their eyes turn blue for 3 seconds then turn green. Then, their hair stands up and turns a mustard-yellow. Their muscles bulge and they become much more menacing.

when they go super saiyan 1:

Son Goku: After Kuririn is killed by Freeza. (DBZ: Frieza Saga)

Son Gohan: While training in the Room of Spirit and Time with Son Goku. (DBZ: Early Cell Saga)

Vegeta: Prior to the 19/20 android battle while training in outer space. (DBZ: Android Saga)

Future Trunks: In the alternate future, #17 and #18 killed Son Gohan causing him to become SSJ. (DBZ: Trunks Special)

Chibi-Trunks: Not determined... most likely while training in Vegeta's gravity room.(DBZ: Majin Buu Saga)

Son Goten: While training with Chichi when he was 6 years old. (DBZ: Majin Buu Saga)

Gotenks: After fusing as SSJs in the Majin Buu Saga. (Majin Buu...)

Brolly: SSJ1: Since birth... (Movie 8)

Super Saiyan Level 2

Second level Saiyan-jins are a step higher and more powerful than the level 1.

The differences are subtle, but are there. Level 2 Saiyans change their eye color to green, and while their hair remains yellow, it is spiked closer together at the top. Their muscles bulge out even more than Level 1s, and they become even more menacing in character. They are also covered in a golden aura of light.

when they go super saiyan 2:

Son Goku: While training in Hell. (DBZ: During the Anoyoichi Budoukai Saga/Beginning of Majin Buu Saga)

Son Gohan: During the fight with Cell. (DBZ: Late Cell Saga)

Vegeta: While training during the 7 years after the Cell Game. (DBZ: Between Cell and Majin Buu)

Gotenks: This is never really noticed... probably either did it after fusing or during the Super Buu fight. (Majin Buu...)

Super Saiyan Level 3

Now we're talking about some serious power here. Super Saiyans at Level 3 become truly a force to be reckoned with and is much harder to attain than going from SSJ1 to SSJ2 (but it's the jump is much more powerful).

If your friend displays the following traits, chances are - they have become a Level 3 SSJ and that you should run for your life IMMEDIATELY the next time you see him/her.

1. They suddenly have green eyes (though this can be a sign of being a SSJ1, SSJ2, or even having a new pair of contact lenses).

2. Their hair stayes yellow but grows down to their legs (though this could mean that they seriously need a hair cut).

3. In a matter of seconds, they have outgrown their clothes with muscles that Mr. T would be proud of. They are constantly training and are FIERCE.

when they go super saiyan 3:

Son Goku: While training in Hell. (DBZ: During the Anoyoichi Budoukai Saga/Beginning of Majin Buu Saga)

Gotenks: Achieved during training in the Room of Spirit and Time. (DBZ: MAJIN BUU!!!!)

Super Saiyan Level 4

What can be more powerful than a SSJ3? What can be make an SSJ3 run for their lives? Why, an SSJ4 of course.

Traits of the SSJ4 are easy to pick up:

1. An SSJ4's eyes turn green, red & brown.

2. Hair turns black & if they got a haircut, their hair grows back the way it originally was.

3. Red fur grows up on their chest.

4. In terms of muscles and fierceness, let's put it to you this way: you'e be better off fighting a nuclear bomb than an SSJ4.

when they go super saiyan 4:

Son Goku: After Son Goku becomes Oozaru in an SSJ state (GT: During the Bebi Saga)

Vegeta: Courtesy of Bulma's Brute Ray, he was able to become a Golden Oozaru and then shrink down. (GT: I believe this was during the Evil Shenlon Saga)

Super Saiyan Level 4: The After Act

Yellow eyes, black-colored hair, and so big (muscle-wise) that... well... I'll leave that to your imagination