Super Saiyan Level 1
This stage was first reached by Goku in movie #6 as he fought Lord Slug. He didn't appear to be a Super Saiyan then, since his hair had a black tinge to it.
Officially, Gokou went SSJ1 for the first time in the Furiza Saga, after Furiza killed Kuririn.
Physical description: Incredibilly increased muscle mass, and his hair turns Goldish/Yellow and Stands up.
*Note* A Saiya-jin is always born with a tail. As long as he keeps his tail, he can turn into a Oozaru (Giant Ape) with a Full Moon.
Super Saiyan Level 2
I personally think Gokou achieved this stage in movie #4, when fighting Cooler. In movie #9, Gohan was told by Gokou to go SSJ2, he tried to go SSJ2, but reached a more incredible stage, The Ultimate SSJ Level, doing so he killed Boujack and the rest of his crew. This level is incredibly more powerful than SSJ1. SSJ1 was used quite frequently in movies #4-9, but SSJ2 had more immediate results. SSJ1 proved inefficient in stopping Boujack's crew, and when Gohan reached SSJ2, he easily overpowered the aliens.
Physical description: Alot greater muscle mass than SSJ1, and a few more inches of blond hair also pointing up. Occasionally accompanied by zapping silver lightning (which happens everyonce in a while)
Super Saiyan Level 3
Gokou first achieved this level during a fight with Majin Buu. This is the most powerful level of Super Saiyan (in what I think of Super-Saiyan). Majin Buu could overpower SSJ3 Gokou, but this level did destroy Fat Janenba in movie #12. SSJ3 was also used in Dragon Ball GT, but Gokou couldn't hold it due to his little body's lack of strength, although he does reach Super-Saiyan Level 4.
Physical Description: Gokou's physical appearance is more lean and menacing looking, with about 4 and half feet of flowing blond hair and a larger muscle mass. Also in this form the Saiyan-jin is Very Quick and Fast.
*Note* Only Gokou and Gotenks have achieved this level. No other Saiyan's have achived it, but others have gone past this level (Vegeta goes SSJ4).
Super Saiyan Level 4
This is actually not a SSJ level, seeing that Gokou and Vegeta doesn't have blond hair. They do have increased muscle mass though, but still, I don't believe this is a SSJ level, and others agree. This is also the only stage with a tail (Well Saiyan-jin already have tails, but they grow it back in this form). In SSJ4, Gokou is almost god-like, and he can use "Times 10 Kame-hame-ha." or "Ultimate Kame-hama-ha
Physical description: Although Gokou was wished by the Dragon Balls to become a child again, in SSJ4 form, he has his normal adult body with a bit more muscle mass. His upper torso is covered in redish/brown fur, his hair is black, and his eyes are red rimmed, pretty wicked actually.
Ahhh yes, Oozaru, when a Saiyan stares at a full moon, he/she will change into a 45-foot tall, monsterous monkey or grollia called a Were-monkey (Oozaru, in Japanese, translates to "Big Monkey). This is possibly the most powerful level under SSJ3. All Saiyan (excluding Gokou and Gohan) will be able to control themselves during this stage (although in Dragonball GT, it is implied that Vegeta couldn't control himself in Oozaru form, but Bebi could.) It doesn't matter which full moon they look at (in Dragonball GT, Gokou turned Oozaru by looking at the full Earth from Space. And, Vegeta had the ability to create a pocket-sized full moon when he first arrived on Earth to fight Gokou and Gohan that made him turn into the Oozaru.)
*Note* A Saiyan must have a tail to be able to turn Oozaru. If the tail is cut off, they revert to normal. If the tail is pulled out by the roots, the Saiyan will not turn Oozaru ever again.
Ougon Oozaru (Golden Oozaru)
A level that was achieved by Gokou 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 Gokou 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 Saiyan-jin, it was also called "Planet Plant", of coarse before renamed to Planet Vegeta