Acarya Nagarjuna (dates of life uncertain; either in the 1st or 2nd centuries CE) is one of the most well-known names in Buddhist history today. His coming was prophesied in the Lankavatara, Manjusrimulakalpa, Mahamegha and Mahabheri sutras, among others.
Born in Vidarbha, legend has it that as a small boy, he had mastered the Vedas and all Hindu science, including magic. As a teenager, he would make two friends and himself invisible, so they could sneak into the local king's royal harem. At the end of one visit, as they were leaving, his two friends became visible again and were caught and executed. Nagarjuna, his world shaken by the loss of his two friends, reevaluated his life and left home to enter a Buddhist monastery in Nalanda, where he became known as Bhikkhu Srimanta, under the Brahman Saraha.
In ninety days he had mastered the Tipitaka, and left the monastery in search of more advanced writings. One day, as he was expounding the Dhamma to a group of people, he saw that two members of the crowd disappeared into the ground. Upon following them, he found himself in the Kingdom of the Nagas, lords of the snakes, who were good buddies of the Buddha himself (when he was alive, some 400 or 500 years or so earlier). The Nagas presented Nagarjuna with a collection of writings, the Prajnaparamita Sutra, that the Buddha (or, in some legends, Ánanda) had delivered but considered too profound for the world at the time, and so was put under the watchful eye of the Nagas until humanity had readied itself for what it contained. The world being ready, Nagarjuna brought the Prajnaparamita to the rest of humanity. This sutra, incidentally, is what gave Mahayana and Hinayana Buddhism their titles: Nagarjuna was one of the fathers of what became Mahayana, and with the sutra's additional wisdom Mahayana ("Greater Vehicle [to Enlightenment]") became known as 'greater' than Hinayana ("Lesser Vehicle"). (Hinayana is now known as Theravada, "Way of the Elders.")
As Sakyamuni is said to have first turned the Wheel of Dhamma (at least, in this kappa), Nagarjuna became the second turning of the wheel. In India, he is considered by many to be a manifestation of Sakyamuni, and so his teachings are regarded as coming from the mouth of Buddha himself. Sadly, there is not much more known about Nagarjuna's life save that he did actually exist, and was known for his vivid philosophical spirit.
Many writings are attributed to Nagarjuna, and even after discarding the ones that are probably or definitely not his creations, we are left with an impressive collection. He wrote theories on schooling, verses on moral conduct, many teachings on Buddhist practice, hymns, books on art, and even pieces on iconography. Among the more important: (summaries coming soon)
The end of his life is not very clear; Tibetan legends say he gave his life to save a friend's. Another legend says that an ant Nagarjuna had accidentally killed with a blade of kusha grass was born in the next life as a contemporary of Nagarjuna, and only he had the power to kill Nagarjuna — which he did, with the kusha grass, even.
Nagarjuna is best known for applying the Buddha's Middle Way to every philosophical standpoint he came across, and reducing them all to glaring contradictions. Rather than denying all these philosophies as false, he asserted that neither existence nor non-existence can be said of anything in the world. Another way of expressing this idea is that there is neither reality as we know it, nor non-reality, but rather just relativity. This contradicted the incumbent school of thought (Sthaviravada), that everything is in a state of constant flux. He also is credited with the idea of sunyata.
The Madhyamika ("Middle Way") tradition grew out of Nagarjuna's work. By the 5th century, two schools of thought had evolved from Madhyamika: Bhavaviveka held that Madhyamika philosophy was inherently positive, but Buddhapalita's strict interpretation held that all standpoints could be reduced to contradiction which directly lead to insight (prajna) and Enlightenment. Buddhapalita's interpretation (along with Chandrakirti's affirmation of it) influenced Tibetan traditions and what would later be called Dhyana (Chinese: Ch'an; Japanese: Zen).
There are many legends associated with Nagarjuna, especially about his early childhood — one says he was destined to die after only seven days, and then after seven years, but he learned mantras to overcome the Lord of Death and was spared. Another says that during a 12-year famine, Nagarjuna sustained the entire monastery at Nalanda with the gold to buy food, because of his knowledge of alchemy, which he had tricked a Brahman into teaching him. His name "Nagarjuna" came from his association with the nagas, and that his skill at spreading the Dhamma was like the accuracy of the famous archer Arjuna.
In some legends, he is said to have discovered the Prajnaparamita because because two people visited the monastery at Nalanda while he served there as abbot. The two people were actually emanations of nagas and sons of the naga king Taksala, and gave off an essence of sandalwood as a protection from human impurities. When Nagarjuna confronted them about this and asked for some sandalwood, they responded that they would have to ask the naga king. When they returned two days later, they said that if Nagarjuna came to the Kingdom of the Nagas, Taksala would do as Nagarjuna wished. When he reached the Kingdom, he was offered many holy and valuable things by the many righteous nagas, and he preached the Dhamma to them in return. They were so pleased that they asked him to stay with them permanently, but having "secur[ed] the Prajnaparamita on 100,000 verses" and gotten naga clay for building stupas, he soid he must return.
He is also said to have built many, many temples and stupas all throughout the nation of Magadha, and provided for them all.
References:
What I remember of a course on Buddhism I took last year
Nagarjuna's Middle Way (bachelor thesis of Jonah Winters): http://bahai-library.org/personal/jw/other.pubs/nagarjuna/
A Biography of Acarya Nagarjuna: http://www.geocities.com/Athens/Ithaca/4886/naga1.htm
Nagarjuna: http://www.akshin.net/philosophy/budphilnagarjuna.htm