The Vishnu Sahasranama (Sanskrit: Viṣṇusahasranāma, विष्णुसहस्रनाम), a tatpurusha compound, is a list of 1,000 names (sahasranama) of Vishnu, one of the main forms of God in Hinduism and the personal supreme God for Vaishnavas (followers of Vishnu). It is also one of the most sacred and commonly chanted stotras in Hinduism. The Vishnusahasranama as found in the Anushasana Parva of the Mahabharata is the most popular version of the 1,000 names of Vishnu. Other versions exists in the Padma Purana, Skanda Purana and Garuda Purana. Each name eulogizes one of His countless great attributes.
The VishnuSahasranāma has been the subject of numerous commentaries. Adi Shankara wrote a definitive commentary on the sahasranāma in the 8th century which has been particularly influential for many schools of Hinduism even today. Parasara Bhattar, a follower of Ramanuja, wrote a commentary in the 12th century, detailing the names of Vishnu from a Vishishtadvaita perspective. Madhvacharya asserted that each name in the sahasranama has a minimum of 100 meanings.
According to the 135th chapter of Anushāsanaparva (verses 14 to 120) in the epic Mahabharata, the names were handed down to Yudhishthira by the famous warrior Bhishma who was on his death bed (of arrows) in the battlefield of Kurukshetra. Yudhishthira asks Bhishma the following questions:
kimekam daivatam loke kim vāpyekam parāyaṇam stuvantaḥ kam kamarcantaḥ prāpnuyurmānavāḥ śubham ko dharmaḥ sarva dharmāṇām bhavataḥ paramo mataḥ kim japan mucyate jantuḥ janmasamsārabandhanāt
In this universe Who is the one (ekam) refuge (parāyaṇam) for all? Who (kim) is the greatest (ekam) Lord (daivatam) in the world (loke)? By eulogising (sthuvantaḥ) whom (kam) can a person (mānavāḥ) reach auspiciousness (śubham) (peace and prosperity)? By worshipping (archantaḥ) whom can a person reach auspiciousness (peace and prosperity)? What (kah) is, in thy opinion, the Greatest Dharma of all Dharmas? By (kim) chanting whose name, can a "creature" (jantuh) proceed beyond (muchyate) the bonds (bandhanāt) of samsāra?
Bhishma answers by stating that mankind will be free from all sorrows by chanting the "Vishnusahasranāma", which are the thousand names of the all-pervading Supreme Being Vishnu, who is the master of all the worlds, the supreme light, the essence of the universe and who is Brahman. All matter animate and inanimate reside in him, and he in turn resides within all matter.
In Sanskrit, sahasra means "a thousand" and nāma (nominative, the stem is nāman-) means "name". The compound is of the Bahuvrihi type and may be translated as "having a thousand names". In modern Hindi pronunciation, nāma is pronounced [na:m]. It is also pronounced sahasranāmam in South India.
There are Sahasranāma for many forms of God (Vishnu, Shiva, Ganesha, Shakti, and others). The Vishnu Sahasranāma is popular among common Hindus, and a major part of prayer for devout Vaishnavas, or followers of Vishnu. While Vaishanvas venerate other deities, they believe that the universe, including the other divinities such as Shiva and Devi, is ultimately a manifestation of the Supreme Lord Vishnu. Followers of Shaivism similarly give prominence to Shiva. Interestingly, despite the existence of other sahasranamas of other forms of God, referring a sahasranama as "The Sahasranama," generally refers to the Vishnu Sahasranama alone, thereby indicating its wide popularity and use.
Two of the names in Vishnusahasranama that refer to Shiva are "Shiva" (names # 27 and # 600 in Adi Sankara's commentary) itself, "Shambhu" (name # 38), "Ishanah" (name #6 4), and "Rudra" (name # 114). Most notably, Adi Shankara, according to one interpretation, has not interpreted these to mean that the deity Shiva and the deity Vishnu are the same. Specifically, he asserts that the deity Vishnu is Brahman itself (not just an aspect of Brahmam). Again, he notes that "only Hari (Vishnu) is eulogized by names such as Shiva", a position consistent with interpretations of the Srivaishnavite commentator Parasara Bhattar. Parasara Bhattar had interpreted Shiva to mean a quality of Vishnu, such as "One who bestows auspiciousness.". In fact, the Shri Rudram, a sacred prayer for Hindus and devotees of Shiva in particular, describes Vishnu as an aspect of Shiva in the fifth anuvaka.
However, this interpretation of the name Shiva has been challenged by Swami Tapasyananda's translation of Sankara's commentary on the Vishnusahasranama. He translates the 27th name, Shiva to mean:"One who is not affected by the three Gunas of Prakrti, Sattva, Rajas,and Tamas; The Kaivalaya Upanishad says, "He is both Brahma and Shiva." In the light of this statement of non-difference between Shiva and Vishnu, it is Vishnu Himself Who Is exalted by the praise and worship of Shiva."  Based on this commonly held Advaitan point of view which has been adopted by Smartas, Vishnu and Shiva are viewed as one and the same God, being different aspects of preservation and destruction respectively. As many Sanskrit words have multiple meanings, it is possible that both Vishnu and Shiva share names in this instance, e.g., the name Shiva itself means "auspicious" which could also apply to Vishnu. The Deities Ananthapadmanabha and Shankaranarayana are worshipped by Hindus, as is Lord Panduranga Vitthala, a form of Lord Krishna with a Shiva Linga on his crown, signifying the oneness of both deities.
Believers in the recitation of the Sahasranama claim that it brings unwavering calm of mind, complete freedom from stress and brings eternal knowledge. A translation of the concluding verses (Phalasruti) of Vishnu sahasranama, state the following: "Nothing evil or inauspicious will befall a man here or hereafter who daily hears or repeats these names.. Whichever devoted man, getting up early in the morning and purifying himself, repeats this hymn devoted to Vasudeva, with a mind that is concentrated on Him, that man attains to great fame, leadership among his peers, wealth that is secure and the supreme good unsurpassed by anything. He will be free from all fears and be endowed with great courage and energy and he will be free from diseases. Beauty of form, strength of body and mind, and virtuous character will be natural to him.... One who reads this hymn every day with devotion and attention attains to peace of mind, patience, prosperity, mental stability, memory and reputation.... Whoever desires advancement and happiness should repeat this devotional hymn on Vishnu composed by Vyasa....Never will defeat attend on a man who adores the Lotus-Eyed One (Kamala Nayana), who is the Master of all the worlds, who is birthless, and out of whom the worlds have originated and into whom they dissolve."
In orthodox Hindu tradition, a devotee should daily chant the Upanishads, Gita, Rudram, Purusha Sukta and Vishnu sahasranama. If one cannot do all this on any day, it is believed that chanting Vishnu sahasranama alone is sufficient. Vishnu sahasranama can be chanted at any time, irrespective of gender.
Varahi Tantra says that in the age of Kali yuga, most stotras are cursed by Parashurama and hence are ineffective. While listing the ones which are free from this curse and hence suitable during Kali Yuga, it is said, "Gita of the Bhishma Parva, Vishnu Sahasranama of Mahabharata and Chandika Saptashati' (Devi Mahatmyam) are free from all Doshas and grant fruits immediately in Kali Yuga."
In a classic astrological text, the Bṛhat Parāśara Horāśāstra, Sage Parashara frequently recommends the recitation of the Vishnu Sahasranama as the best remedial measure for planetary afflictions. For example, see the following verse: "The most effective and beneficial remedial measure for the prolongation of longevity and to obtain relief from other evil effects is recitation of Vishnu Sahasranam." ch 56 verse 30
Sage Parashara mentions this practice more than ten times in his text. Here's another verse:
"The remedial measure to obtain relief from the above evil effects, is recitation of Vishnu Sahasranama." ch 59 verse 77
It is customary to commence the Vishnu sahasranama with a devotional prayer to Vishnu.