Hiranyaksha belonged to a family that would cause Vishnu to incarnate three times to destroy his brother as well as their great grandson, and then the two demons were reborn twice more and each time Vishnu had to deal with them in some sort of eternal cosmic ritual of incarnation. The brothers are supposed to be the famous twin gatekeepers of Vishnu's heaven, Jaya and Vijaya, cursed to fall from grace and find salvation only in opposition to Vishnu. Enmity to the great god would cause their deaths at his hands, which automatically meant salvation. They were first born as Hiranyaksha and Hiranyakashipu, the latter killed by the Narasimha avatar. Then they incarnated as Ravana and Kumbhakarna, both slain by Rama and finally in the Mahabharatha as the nonentities Shishuplala and Dantavakra, duly put away by Krishna. The demons seem to be some sort of universal destabilizing principle, which Vishnu had to remove to restore equilibrium in the universe. That they are the gatekeepers, guardians of the threshold to Vishnu, sustainer and integrative principle of the universe, is significant in mythological terms. It is only by passing through chaos that you come to the still center of the universe.

Some texts take the story of this incarnation further. Bhoodevi, having being embraced so long by Vishnu in the rescue became his wife by default, there was no other resolution to potentially outraged proprieties. The result of this union was Narkasura, a great and mighty warrior who lived for eons as a righteous king but finally went to the bad, launched a campaign of world conquest, and had to be slain by Krishna. As to the terrifying psychological connotations about such blatant patriarchal homicide of an overachiever son, India has always been on the side of the narcissistic impulses of the parent. Narkasura was 'wrong' in desiring to so become prominent when his 'father' was still alive - and his death is regarded as just desserts, though dressed up in pious fatuities about liberation by being slain by the hand of god.

The Shaiva texts added a further spin on the Varaha incarnation. Having accomplished his missions, Vishnu decided to spend some time in this new and playful form. Alas, he underestimated the power of the brute consciousness in reasserting itself and he came to identify himself with the Boar. He met a beautiful sow somewhere and they set up house and had many piglets. Shiva, seeing the appalling degradation of the great Vishnu, attacked the boar and flayed its pelt - upon which the fully conscious and awakened Vishnu rose up in his remembered glory. Shiva is the embodiment of Pure Consciousness, which is why as Nataraja he dances in triumph upon the demon Apasmara - Amnesia. His restoring Vishnu to full awareness, by removing his covering of amnesia, symbolized by the hide of the boar, is thus well in character and psychologically astute. Apart from an obvious childish attempt to assert the supremacy of Shiva, the story is insightful in the perils of accessing lower levels of consciousness. They may become necessary sometimes, to release the great amounts of strength needed for fearful tasks, but if persisted in, they devour the higher faculties of the mind and consciousness - and man sinks back to brute levels, literally as content as a pig in the mud. In some versions, to drive home this point with greater intensity, it is Shiva who incarnates as a boar and Vishnu who rescues him from porcine happiness. There is never any single version of any myth in India.

The allegorical interpretations of the entire myth have always been very popular with the more thoughtful amongst the ancient commentators. In this point of view the entire story is a recreation in hyperbolic terms of a massive Yagya, a ritual intervention made by the wise of the earth when they deem that sinfulness has assumed threatening stature. The body of the Varaha is thus a manifestation of the Yagya itself. The words used in eulogy are very revealing in that the writers of the Bhagvata knew this myth was not to be taken solely at a literal level.

"You alone exist, the supreme condition of being, Kesava, Lord of the Universe. You are the Purusha (Cosmic Man and the first to institute Yagya) of the sacrifices; your feet are the Vedas; your tusks the stake to which the sacrificial offering is bound; your teeth are the oblations; mouth the altar; the tongue is the fire and the hairs of your body are the sacrificial grass. Your eyes, oh omnipotent Lord, are day and night, your head the seat of Brahma, your name is the content of all the hymns of the Vedas, your nostrils are all the oblations. The snout is the ladle of sacrifice, the deep voice the chanting of the Sama-Veda, the massive body the hall of sacrifice, the joints the various ceremonies; the ears are the rites, both compulsory and optional..." and so on.

It is evident therefore that the Varaha aspect of Vishnu seemed to tap into some deep reservoir of the Hindu psyche considering the immense amounts of cultural output it has engendered. As said before the Varaha was never worshipped, the rendering of homage to the avatars in themselves, as distinct from Vishnu, beginning with Narasimha alone. Nevertheless it remains a primal myth of the Hindu imagination, encompassing many of its core concerns simultaneously.

Addendum
We have recently come to know that there is a small temple dedicated to the Varaha Avatar form of Vishnu in Simhachalam which is near Vizag town in Andhra Pradesh state in India. At the famous Tirupati Balaji temple there is a convention that the full fruits of pilgrimage can be gained only after visiting the small shrine dedicated to Varaha found over there. The Varaha Avatar is therefore still obviously worshipped only in the Andhra Pradesh area.