Goku Kid Form (Wish From Red Shenron)

Emperor Pilaf wishes Goku back into a child in the beginning of Dragon Ball GT. In this form, it is harder for Goku to maintain more powerful forms, such as Super Saiyan. While a child he was able to get his tail back, with the help of Elder Kai.
Goku in Great Ape Form

Like all Saiyans, Goku can transform into a Great Ape (Oozaru) when he sees the full moon while he possesses his tail.
Goku in Golden Great Ape

Goku achieved this form in Dragon Ball GT after Elder Kai helped Goku to grow back his tail which allowed him to once again transform into a Great Ape. When he looked at the earth in the Baby Saga, its sufficient substitute Blutz waves allowed him to take this form, a combination of the Super Saiyan state and the classic Great Ape transformation. Upon regaining control, he later transformed into Super Saiyan 4, his strongest form yet.
Goku in False Super Saiyan
During the fourth Dragon Ball Z movie, Lord Slug, Goku achieved this form in an attempt to defeat Lord Slug. Through rage of being beat down Goku unleashed a huge amount of aura and became this false like Super Saiyan which gave him more speed and strength for a couple of seconds. His looks are like Kaio-ken except his eyes are white like Broly's and his hair stands up.
Super Saiyan Goku

Goku uses his new power to defeat Frieza, the antagonist of the series at the time. Frieza had destroyed the Saiyans out of his fear of their growing power, and the idea of a possible "Super Saiyan". As a result of defeating Frieza, Goku avenges the Saiyan race, and the death of his best friend Krillin.
Super Saiyan Kid Goku

After being wished into his childhood form, Goku can still transform into a Super Saiyan. However, he is unable to maintain the form for as long as he can in his adult body.
Ascended Super Saiyan Goku

Like the Ascended Super Saiyan form, Goku achieves this form in the Hyperbolic Time Chamber while training with Gohan. Although apparently stronger than Cell in this state, Goku told Gohan he could not defeat him because Cell was much faster, because "all the power in the world would do no good if you can't even hit the guy." Instead of persevering harder to simply increase power output, Goku decides that simply mastering the Super Saiyan form to suppress its downsides and make it a natural state is the best way to fight and gain power. This form is never used after its inital unlocking along with Ascended Super Saiyan, as a result.
Ultra Super Saiyan Goku

Like the Ascended Super Saiyan form, Goku achieves this form in the Hyperbolic Time Chamber while training with Gohan. Although apparently stronger than Cell in this state, Goku told Gohan he could not defeat him because Cell was much faster, because "all the power in the world would do no good if you can't even hit the guy." Instead of persevering harder to simply increase power output, Goku decides that simply mastering the Super Saiyan form to suppress its downsides and make it a natural state is the best way to fight and gain power. This form is never used after its inital unlocking along with Ascended Super Saiyan, as a result.
Super Saiyan 2 Goku

Although it is unknown when exactly Goku achieved this state of Super Saiyan, it is assumed Goku achieved this transformation in the Other World as he could put unlimited energy into his transformation. It was first seen when fighting Majin Vegeta's own Super Saiyan 2 form in their epic battle during the Buu saga, Goku transforms into this state before showing the Super Saiyan 3 transformation to Majin Buu and Babidi, and again in an anime filler where he begins to fight Kid Buu. In Dragon Ball GT, Goku can be seen briefly transforming into a Super Saiyan 2 while deflecting an attack by General Rilldo, and before he transforms into a Super Saiyan 3 during his second fight with Super Baby Vegeta. He also uses the form during the 12th and 13th movies.
Super Saiyan 3 Goku

Goku achieved this level in Other World as he could put unlimited energy into his transformation. Goku is first seen using this transformation against Majin Buu during the Majin Buu Saga. Once in this form, Goku was able to easily overpower Majin Buu in his first form and fight more than evenly with Kid Buu despite a heavy ki drain taking its toll on him. It is said by Vegeta and Goku himself that if Goku had been using the Super Saiyan 3 at its maximum potential, he would have been able to defeat Kid Buu. However, the transformation is extremely draining in terms of energy, as it cut Goku's time in half or lower. He is also unable to regather his energy whilst in a living body, making it impractical to use it out of the Other World.
Super Saiyan 3 Kid Goku

After being wished back into his childhood form, Goku is still able to transform into a Super Saiyan 3. However, he is only able to maintain the form for a few minutes. This form is not enough to defeat Baby Vegeta, so Goku is forced to recruit help from Elder Kai, which leads to his Golden Great Ape transformation.
Super Saiyan 4 Goku

This form is achieved by Goku after achieving the state and being calmed by Pan.The overwhelming power of this transformation is apparently great enough to overcome Goku's transformation into a child by Red Shenron. The spell is only dispersed during the transformation, however. In addition to him being turned back into an adult temporarily, Goku's overall appearance changes yet again. His tail is easily visible, the hair is longer than when in his normal state (not nearly as long as a Super Saiyan 3, though), his eyes become lined (much like Vegeta's did when he was a Majin in the Majin Buu Saga), his eye color is now golden yellow, and fur covers almost all of his body from head to toe. His clothes change from his childhood garb, leaving him only dressed below the waist (excluding his armbands). As a Super Saiyan 4, Goku is able to easily surpass all but the most powerful enemies in the final parts of Dragon Ball GT. But at the end of the last episode of Dragonball GT his tail disappears again, and it is unknown if he could ever transform to this state from then on.
Super Saiyan 5 goku (ssj5)

Is there a super saiyan 5?
NO, there is no Super Saiyan 5, for the basic reason that there is no Super Saiyan 4. When Toriama decided to stop Dragon Ball, he said he wanted no more episodes to be made, he said it should end with Buu, but the gap would have been left in the commercial business, and so others tried to milk it. It is no coincidence that there were over 200 episodes of Dragon ball z, and barely 60 of GT. They took it to extremes with extra fusions, Omega shenron, Super Saiyan 4, descendants, such as goku junior. A master piece was butchered with gt, the magic was lost.
Toriama originally wanted to stop dbz after Frieza was destroyed, but he was persuaded to continue. Of course, Cell and Bu were great villains, but the magic and historic awe we ll shared from the frieza saga was absent. however, it was still brilliant. Like all geniuses, he knew when to end it, and that is before it goes to cheesy and comercial extremes. others did that for him.
Treat GT, like you would treat foreign occupation.