"And this...is to go even further beyond"
-GokuSuper Saiyan 3 is the strongest of all Super Saiyan forms in the manga, and the Dragon Ball Z anime. It is the third form of Super Saiyan, the successor to the first and second transformations. Goku was the first to achieve the form, doing so in his vigorous seven years of training in Other World. Where the third stage of Super Saiyan's purpose was 100% utilization of physical stamina, the purpose of the Super Saiyan 3 transformation is to increase the utilization of ki, and as a result, the transformation rapidly consumes the energy of the user. This notably leads to extended levels of fatigue, even long after powering down. If the user has died and is not encumbered by a living body, this strain is reduced somewhat, and additional energy depletion is minimized (such as in Goku's case during his first fight with Majin Buu). The difference between Super Saiyan 3 and Super Saiyan 2, its predecessor, are immediately noticeable as speed, strength and endurance are all pushed far beyond the normal limits. The first time that Goku used this form on Earth, its power caused massive tidal waves and hurricanes and nearly shook the planet apart. During subsequent transformations, Goku seemingly controlled it enough to prevent such dangerous side-effects. In addition, this power could be sensed even as far as the distance between Earth and Supreme Kai's planet, something that not only shocked Supreme Kai, Kibito, and Gohan, but worried them as well. According to the Daizenshuu, the Super Saiyan 3 form gives the user four times the strength of a Super Saiyan 2.
Super Saiyan 3 Goku fighting Kid Buu Added by BeadtmdcHowever, with the enormous power, there are some very serious setbacks stemming from the rapid use of ki energy. When the then-deceased Goku showed Babidi and Majin Buu the form, he cut his remaining temporal revival energy in half, and in the anime when he shows his power to the excited Trunks and Goten, his energy was completely dissipated, forcing him to return to Other World.
Likewise, when the now fully living Super Saiyan 3 Goku attempted to regain energy while Vegeta and Mr. Satan distracted Kid Buu, he was unable to do so, draining his power completely and leaving him in a weakened, normal state where he could not even control the Spirit Bomb. Goku acknowledged that he had little experience with the transformation, with his fight with Kid Buu being the first time he used it in a full fight with a living body. Performing it twice in a short time brought him to his knees and expended all of his remaining energy. (In the manga, he does not revert to his original form until after Vegeta intervenes to buy him the minute that he needed, however.) The fused Gotenks did not seem to exhibit such drawbacks, though if he had more time beyond his one hour of fusion to use the state, the same energy drain could have conceivably taken place.
The energy drain issues are exacerbated even further when Goku is turned back into a child in Dragon Ball GT, where he can only hold the transformation for a couple of seconds and struggles to utilize the power in fights with General Rildo and Baby Vegeta. This limit was lifted somewhat after Goku's tail was restored with the help of Elder Kai, allowing him to sustain the form for a longer duration, though he was still no match for Super Baby Vegeta in this state.Goku first used the Super Saiyan 3 transformation in a brief battle against Majin Buu in order to stall him long enough for Trunks to find the Dragon Radar. He was able to overtake the monster, completely outmatching him blow for blow, though the obese version had yet to freely demonstrate his full power by getting angry at the time. He eventually retreated from the fight, as he wanted Goten and Trunks to defeat Buu with their fusion technique, as he "wouldn't be around forever." Goku later stated he believed he could have killed Buu if he really tried, but held complete faith in Gotenks' ability to destroy him if they were to try the Fusion Dance as Super Saiyans.
This form was next seen used by Gotenks, the fusion between Goten and Trunks, during his fight with the new, more powerful version of Majin Buu. While in the Hyperbolic Time Chamber, Piccolo destroyed the only entrance in or out of the dimension, in hopes of trapping Super Buu inside, when he believed that Gotenks had lost and that the universe would be destroyed. Unfortunately, Super Buu was able to escape by ripping the dimensions open using intense sound waves from his own voice when he became angry at the thought of not having anymore food to eat. Learning from the things that Goku taught him about being Super Saiyan 3, Gotenks transforms into Super Saiyan 3 and rips up a hole in a similiar fashion, shocking Piccolo. Once outside, Gotenks battled Super Buu in earnest. The two appeared to be an even match, with Gotenks appearing to gain the upper hand before the fusion broke.