- Cleanses one's mind from all evil thoughts
- Provides benefits like Firmness of mind, good memory, happiness of the self (inner happiness), and freedom from anger, jealousy, and greed
- Mitigates misery, sorrow and grief
Bhishma – "Man who hears the names every day or who recites them every day, never meets with any evil either here or hereafter"
Adi Sankaracharya – said that the Sahasranama bestowed all noble virtues on those who chanted it
Parasara Bhattar, a follower of Ramanujacharya had said that Vishnu Sahasranama absolves people of all sins and has no equal
The Final Word Sage Vedavyasa concludes the Stotram with the assertion - twice stated - that there is no way a devotee of Vishnu can meet with any dishonor or disgrace of any kind (na te yanti parabhavam - ne te yanti parabhavam om nama iti).
Wikipedia page is a great start. It also contains other links.