The Vishnu Sahasranamam refers to the thousand names of the Lord Maha Vishnu. The reference to Vishnu Sahasranama is found in the great Epic Mahabharata written by Veda Vyasa. In Sanskrit, 'sahasra' means 'a thousand' and 'nama' means 'name'. Together these words may be translated as 'having thousand names'. After the Kurushetra war, Yudishtira was appointed King. Bheeshma who wanted to die at the feet of Lord Krishna was lying in the bed of arrows when finally Krishna accompanied by the Pandavas arrived to meet him. Before leaving his mortal body, Bheeshma gives a long discourse to Yudhisthira on various aspects of life and Dharma. It was then Yudishtira asked six questions to Bhishma one of which was as to who the Supreme God was and whose praise and worship was sure to bring salvation. Bheeshma, in response gave the thousand names of Lord Vishnu. One unique feature of this event is that the answer was given in the presence of Lord Krishna, the avatar of Maha Vishnu.

Vishnu Sahasranam is one of the most sacred and chanted stotra by many Hindus, especially those belonging to the Vaishnavite sect. It is said that a Hindu devotee should daily chant the Upanishads, Bhagavad Gita, Rudram, Purusha Sukta and Vishnu sahasranama. If one cannot do all this on any day, it is believed that chanting Visnu sahasranama alone is sufficient. Vishnu sahasranama can be chanted at any time, irrespective of gender. It is believed that Recitation of this stotra eradicates all evil and help reconnect with the divine within. Anyone who chants with devotion and perseverance recites these names wholeheartedly will be free from all fears at any time and disease never afflicts him. The recitation of the Sahasranama is said to bring calmness of mind, courage, fame, freedom from stress and eternal knowledge. However, one aspect to be noted is the fact that three of the names in Vishnu sahasranama (Shiva, Rudra and Shambu) refers to Lord Shiva. In the same manner Shri Rudram, one of the most sacred prayers for Hindus especially the Shaivites describe Vishnu as an aspect of Shiva. The famous Indian philosopher Adi Sankaracharya interpreted this to mean that Vishnu and Shiva are the same and it is Vishnu that is praised by worship of Lord Shiva. Another possibility is that Lord Vishnu and Lord Shiva maybe sharing those names as many Sanskrit words have multiple meanings. Another interpretation is that the names "Shiva" and "Rudra" in Vishnu sahasranama refers to the qualities or attributes of Maha Vishnu and do not indicate that Vishnu and Shiva are one and the same God. However some like to think that Vishnu and Shiva are one and the same God, being different aspects of preservation and destruction respectively. What ever the case is I like to believe that whether there is thousand names or thousand forms it all points to the only one ultimate God.

Also see

Vishnu Mantras 

Avatars of Lord Vishnu (1-6) - Part 1 

Avatars of Lord Vishnu - Part 2