Orthodox Hindu Schools
As anyone familiar with the orthodox Hindu darshanas knows, a belief in God is not a central feature of all orthodox schools of thought. Two of the orthodox Darshanas in particular seem distinctly rooted in materialism: Samkhya and Vaisheshika. Those are discussed below.
Chattopadhyaya goes so far as to claim that:
“If the Sankhya philosophy were in the earlier times an explicit philosophical re-statement of the fundamental theoretical position implicit in Tantrism, and, if further, as we have aready tried to argue, the term Lokayata originally stood for the beliefs and practices broadly referred to as Tantrism, then original Sankhya may be viewed as the most important developmet of the Lokayata tradition in Indian philosophy. Silamka, the Jaina commentator, was justified in denying any basic difference between Sankhya and Lokayata. Sankara, too, made the Sankhya philosophers quote the authority of the Lokayatikas”
This view is slightly bolstered by the fact that Samkhya originated in northeast India, the densest area of Lokayata/Tantra presence. The Samkya–Karika and Shankara both agree in identifying Samkhya as a form of Tantra.  Samkhya use of the purusha body analogy is also similar to the Tantra view of the human body as a microcosm of the universe. However even if we reject Chattopadhyaya’s extreme statement of Samkhya’s Lokayata lineage claim, there is reason to suspect that Lokayata contributed to the development of Samkhya philosophy.
Samkhya was the earliest codified Brahminical school, (c. 600 BC) as both modern and ancient scholarship confirms. Samkhya was an atheistic or agnostic system based on the pursuit of knowledge through logic. Much as it was a response to materialism, it was also a response to the “supernatural authority and ritualistic ethics of the Brahmanas.”  In the manner of many Indic philosophies, from Advaita Vedanta to Jainism, to Neo-Vedanta, Samkhya seems to have adopted major elements of both the schools it was directly responding to. Riepe explains the phenomenon poetically: …it is a combined attempt to give a philosophical kiss to orthodoxy and yet incorporate some of the tendencies of materialism and naturalistic heterodoxy.”
A possible Samkhya attempt to merge Lokayata with Vedic philosophy is most obvious in the realm of epistemology. Samkhya accepts only three pramanas: (valid means of acquiring knowledge) perception, inference, and valid testimony (aptavacana ) While aptavacana has often been interpreted as unqualified support of revelation, the Samkhyas themselves deny this: “By saying true revelation, all pretended revelations such as those of Sakya, Bhikshu, &c., have been set aside. The invalidity of these systems is due to their making unreasonable assertions, to want of sufficient basis, to their making statements contradictory to proofs…”
In other words, Samkhyas supported testimony as a form of inference, and furthermore justified inference as a form of perception. Of the Samkhya pramanas, the Lokayatas generally support perception and inference, but reject testimony. Samkhyas seem to be trying to lead Lokayatas into accepting scriptural authority by building an epistemology the basis of which the Lokayatas already accepted.
Their theory of causality is essentially the same as the Lokayata one. They both adhere to a form of Svabhavavada meaning that nature is its own cause (though in the Samkhya version, karma is included as a natural or physical process governed by the movement of atoms.) The following three Samkhya quotations conform exactly to the Lokayata viewpoint. From the Mahabharata’s Shanti–Parva, as quoted by Singh : Any solid metal heated in fire dries up water when coming in contact with it. Likewise, the material body produces the mind and its attributes of perception, memory, imagination, etc. As the lodestone moves iron, likewise the senses are controlled by the mind” From Kapila:
There cannot be the production of something out of nothing (na-vastuno vastu-siddhih); that which is not cannot be developed into that which is. The production of what does not already exist (potentially) is impossible, like a horn on a man; because there must of necessity be a material out of which a product is developed; and because everything cannot occur everywhere at all times; and because anything possible must be produced from something competent to produce it
And finally, from Dasgupta retelling a section of the Mahabharata in which the Samkhya viewpoint is described: “‘It is said that as Rahu (the shadow of the sun during an eclipse) cannot be seen apart from the sun, so the Self cannot be seen apart from the body.’ The Selfs (saririnah) are spoken of as manifesting from the prakriti.” The obvious similarities between the schools didn’t escape Shankara, who cites arguments against Lokayata to attack Sankhya identification of intelligence with the body
Samkhya also makes drastic concessions to the critics of the Vedas, by admitting that they are not eternal, that their truth must be established by reason. The single point of divergence between Samkhya and Lokayata is regarding the soul. Whereas the Lokayata believe that the soul either does not exist, or is identical to the body, the Samkhya believe that the soul is the single thing in the universe, which is composed of Prakriti, or universal consciousness. It is the sole facet of idealism in their system. Everything else in the universe, including one’s mind, is composed of Purusha, or matter, to which materialism and logic apply. This is the bargain struck by Samkhya between materialism and idealism.
There is also at least one supposed instance of a Lokayata practitioner, Asuri, converting to Samkhya and becoming one of its principal teachers.   Later theistic Samkhyas seem to blame Asuri for the sect’s atheism. Despite its idealist shift, Samkhya did retain many of the above concessions to Lokayata. The causality and ontology of Samkhya are in the Bhagavad Gita, and though modified by Vedanta, survive today in modern Advaita Vedanta Hinduism. The system of three gunas as explained in the Bhagavad Gita is also Samkhya in origin, though it was originally used to describe and explain the motion of atoms. Even in its current form though retains its Svabhavavada meaning. According to Garbe, Thomas, and Sastri, Samkhya was also the originating system of Buddhism, though this theory relies on Sankhya having existed long before its first known text. There is even reason to believe that Yoga emerged from Samkhya. Yoga essentially adopts the Samkhya Purusha/Prakriti ontology, and adopts the body-as-universe metaphor of early Vedic thought, and breath-magic in a practical way very akin to Tantrism.
Making the case that Vaisheshika emerged from Lokayata is much more difficult, as we have no record of conversions, and it doesn’t seem associated with Tantra. However, in its early stages the similarities were pronounced enough that it is worth mentioning.
Epistemologically early Vaisheshika corresponds extremely well with Lokayata. It only accepted two pramanas; perception and inference. Testimony was eventually included as a form of inference, much like Samkhya rationale. Ontologically the similarity is equally obvious. Early Vaisheshika had 4 classes of atoms; initially (though ether seems to have been quickly added.) These atoms obeyed a form of Svabhavavada, insofar as their movement, conjunction, and disjunction could be fully explained by their inherent qualities. Even the conscious mind is a product of atoms and their qualities, not a product of the soul. This of course was a major point of contention between the Advaitas and Samkhyas. Interestingly, this belief leads the Vaisheshikas into a kind of deterministic deism, with the atman setting all atoms in motion at the onset of the universe.
However, there are no explicit records of Vaisheshikas converting from Lokayata, nor of their strength in the northeast, nor of their connection to Tantra. In short, there simply isn’t enough information to determine how much influence Lokayata had on Vaisheshika, especially considering their later merger with the Nyaya school which resulted in drastic philosophical modifications and textual additions.
Chattopadhyaya, Lokayata: A Study in Ancient Indian Materialism, 362.
Krishna Ishvara, The Samkhya–Karika, comment. Gaudapda, trans. Har Dutt Sharma, (Poona: Oriental Book Agency, 1933) http://www.easterntradition.org/samkhya karika.html (accessed October 25, 2013), 80.
Chattopadhyaya, Lokayata: A Study in Ancient Indian Materialism, 360-361.
Th’U bkwan blo-bzang Chos Kyi-Nyi-ma, A Tibetan Eye-View of Indian Philosophy, trans. Kewal Krishan Mittal, (New Delhi: Munshiram Manoharlal Publishers, 1984), 23, 96.
Dale Riepe, The Naturalistic Tradition in Indian Thought, (Westport: Greenwood Press, 1982), 181.
 Riepe, The Naturalistic Tradition in Indian Thought, 183-184, 181.
 Riepe, The Naturalistic Tradition in Indian Thought, 184.
 Riepe, The Naturalistic Tradition in Indian Thought, 189-190.
Bhagwan B. Singh, “Commentary on Gerald J. Larson’s “The Notion of Satkārya in Sāṃkhya” and Frank Podgorski’s “Śaṃkara’s Critique of Sāṃkhyan Causality in the Brahmasūtra-bhāṣya,” Philosophy East and West, 25, no. 1 (1975): 61, http://www.jstor.org/stable/1398433 (accessed October 25, 2013).
Singh, “Commentary on Gerald J. Larson’s ‘The Notion of Satkārya in Sāṃkhya’ and Frank Podgorski’s ‘Śaṃkara’s Critique of Sāṃkhyan Causality in the Brahmasūtra-bhāṣya,'” 61.
 Riepe, The Naturalistic Tradition in Indian Thought, 196.
Chattopadhyaya, Lokayata: A Study in Ancient Indian Materialism, 400.
Chattopadhyaya, Lokayata: A Study in Ancient Indian Materialism, 397.
P.T. Raju, Structural Depths of Indian thought, (Albany: State University of New York Press, 1985), 88.
Randall Collins, The Sociology of Philosophies, (Cambrige: The Belknap Press of Harvard University Press, 2002), 904.
Swami Prabhananda, ed. “The Problem of God in Samkhya Philosophy,” Bulletin Of Ramakrishna Mission Institute Of Culture, 54: 163.
Chattopadhyaya, Lokayata: A Study in Ancient Indian Materialism, 369.
Satyavrata Ramdas Patel, Hinduism: Religion and Way of Life, (Associated Publishing House, 1980), 31-32.
Gopi Nath Kaviraj, Kaviraja Abhinandana Grantha, (Delhi: Motilal Banarsidass, 1967), Introduction.
Gradinarov Plamen, “Anthropic Web of the Universe: Atom and Atman,” Philosophy East and West, 39, no. 1 (1988): 38, http://www.jstor.org/stable/1398879 (accessed October 26, 2013).
William M. Indich, Consciousness in Advaita Vedanta, (Delhi: Motilal Bandarsidass, 1995), Electronic edition, 29.