This is a comprehensive collection of Hindu source texts (1). Click on the links above to view each section.
The four Vedas are the primary texts of Hinduism: the Rig Veda, Sama Veda, Yajur Veda and Atharva Veda. They also had a vast influence on Buddhism, Jainism, and Sikhism. The Rig Veda, the oldest of the four Vedas, was composed about 1500 B.C., and codified about 600 B.C. It is unknown when it was finally committed to writing, but this probably was at some point after 300 B.C.
The Vedas contain hymns, incantations, and rituals from ancient India. Along with the Book of the Dead, the Enuma Elish, the I Ching, and the Avesta, they are among the most ancient religious texts still in existence. Besides their spiritual value, they also give a unique view of everyday life in India four thousand years ago. The Vedas are also the most ancient extensive texts in an Indo-European language, and as such are invaluable in the study of comparative linguistics.
The Rig-Veda translated by Ralph Griffith  This is a complete English translation of the Rig Veda.
The Sama-Veda translated by Ralph Griffith  282,861 bytes.
The Sama Veda is a collection of hymns used by the priests during the Soma sacrifice. Many of these duplicate in part or in whole hymns from the Rig Veda. This is a complete translation.
The Yajur Veda translated by A.B. Keith 
This is a complete translation of the Yajur Veda. The Yajur Veda is a detailed manual of the Vedic sacrificial rites.
The Atharva-Veda translated by Maurice Bloomfield  (Sacred Books of the East, Vol. 42)
The Atharva Veda also contains material from the Rig Veda, but of interest are the numerous incantations and metaphysical texts, which this anthology (part of the Sacred Books of the East series) collects and categorizes. The Atharva Veda was written down much later than the rest of the Vedas, about 200 B.C.; it may have been composed about 1000 B.C.
A Vedic Reader for Students by A.A. Macdonell  (excerpts) 121,143 bytes
This text serves as an introduction to the dramatis personae of the Rig Veda.
Max Müller, translator  (Sacred Books of the East, vols. 1 and 15)
The Upanishads are a continuation of the Vedic philosophy, and were written between 800 and 400 B.C. They elaborate on how the soul (Atman) can be united with the ultimate truth (Brahman) through contemplation and mediation, as well as the doctrine of Karma– the cumulative effects of a persons’ actions.
Other Primary Texts
The Laws of Manu George Bühler, translator  (Sacred Books of the East, vol. 25)
Manu was the legendary first man, the Adam of the Hindus. This is a collection of laws attributed to Manu.
The Dharma Sutras George Bühler translator  (Sacred Books of the East, Vol. 2)
This is the first half of the Dharma Sutras, another set of law books by various scholars from the first millenium B.C.
The Institutes of Vishnu Julius Jolly, translator  (Sacred Books of the East, Vol. 7) This is also one of the law books of Hinduism. It contains several notable passages, including descriptions of yogic practises, and a moving hymn to the Goddess Prajapati.
The Mahabharata and Ramayana are the national epics of India. They are probably the longest poems in any language. The Mahabharata, attributed to the sage Vyasa, was written down from 540 to 300 B.C. The Mahabharata tells the legends of the Bharatas, a Vedic Aryan group. The Ramayana, attributed to the poet Valmiki, was written down during the first century A.D., although it is based on oral traditions that go back six or seven centuries earlier. The Ramayana is a moving love story with moral and spiritual themes that has deep appeal in India to this day.
In addition, a key Hindu sacred text, the Bhagavad Gita, is embedded in Book Six of the Mahabharata.
The Mahabharata, translated by Kisari Mohan Ganguli [1883-1896]
Rámáyan Of Válmíki translated by Ralph T. H. Griffith [1870-1874]
This is the first complete public domain translation of the Ramayana to be placed online.
The Ramayana and Mahabharata R. Dutt translator 
A very readable abridged version of these epics.
Indian Idylls, Sir Edwin Arnold, translator  279,713 bytes
More stories from the Mahabharata, rendered in poetry.
The Bhagavad Gita, usually considered part of the sixth book of the Mahabharata (dating from about 400 or 300 B.C.), is a central text of Hinduism, a philosophical dialog between the god Krishna and the warrior Arjuna. This is one of the most popular and accessible of all Hindu scriptures, required reading for anyone interested in Hinduism. The Gita discusses selflessness, duty, devotion, and meditation, integrating many different threads of Hindu philosophy.
The Bhagavadgîtâ with the Sanatsugâtîya and the Anugîtâ translated by Kâshinâth Trimbak Telang, (Sacred Books of the East, Vol. 8) 
This is a scholarly prose translation of the Bhagavad Gita with two other similar, less well known, works from the Mahabharata.
The Bhagavad Gita A modern prose translation, sanctioned by the International Gita Society.
The Bhagavad Gita Sir Edwin Arnold, translator  A classic poetic version of the Gita.
The Vedântâ-Sûtras, with commentary by Râmânuja, translated by George Thibaut; (Sacred Books of the East, Volume 48) 
The Vedântâ-Sûtras, with commentary by Sankarâkârya, translated by George Thibaut; Part I (Sacred Books of the East, Volume 34) 
The Crest-Jewel of Wisdom and other writings of Śankarâchârya; translation and commentaries by Charles Johnston [1946, copyright not renewed]
The S’rimad Devî Bhâgawatam translated by Swami Vijnanananda (Hari Prasanna Chatterji) 
The Devî Gita translated by Swami Vijnanananda (Hari Prasanna Chatterji) 
The Song of the Goddess. This is an excerpt from the S’rimad Devî Bhâgawatam (above)
The Yoga Sutras of Patanjali – This concise work describes an early stage in the philosophy and practise of Yoga. Dating from about 150 B.C., the work shows dualist and Buddhist influences. The Yoga Sutras are required reading if you are interested in Yoga and meditation.
The Sánkhya Aphorisms of Kapila
translated by James R. Ballantyne 
Râmakrishna, His Life and Sayings
by F. Max Müller 
(1) Source texts on this page are provided courtesy of Theology101.org