Super Saiyan 3 is the third form of Super Saiyan a Saiyan can take, directly following Super Saiyan 2.. In a way, Super Saiyan 3 is the final form of Super Saiyan, since Super Saiyan 4 is the stage after Golden Oozaru and not Super Saiyan 3. Unlike Super Saiyan 1 and 2, Super Saiyan 3 cannot be sustained forever, even after mastering it. It's power is about as strong as Majin Buu.
A Super Saiyan 3's hair becomes extremely long, reaching down past their waist. They also lose their eyebrows. Aside from the hair, there are no other notable changes.
The original user of the Super Saiyan 3. He is the first to use it, the first to master it, and generally the first to obtain new forms of each stage of Super Saiyan. It is safe to say that Goku is the master of the Super Saiyan.
Vegeta was the third Saiyan to achieve Super Saiyan 3.
Neither Gohan nor Goten can use Super Saiyan 3. Though since they have both mastered Super Saiyan 2, after fusing they can use Super Saiyan 3.
Bardock learned Super Saiyan 3 after watching his son use it in the afterlife.