That's a hard question to answer about recent books. Some might suggest Al Gore's writing, although it seems to me that his winning of the Nobel Peace Prize merely shows how politicized the Scandinavian awards have become.
The further back we go, the easier it is to see benefits. For example, The Federalist Papers (Madison, Hamilton, Jay) and The Wealth of Nations (Adam Smith) were two books that influenced people to make political and economic changes that have proven beneficial. Reflections on the Revolution in France (Edmund Burke) was helpful in increasing understanding of what not to do.
All three of those books are often classified as "great," but we should also note the big difference between "greatest" (or "best") and "most beneficial." For example, George Orwell's 1984 and Animal Farm aren't great novels, but they were certainly beneficial as the Cold War began in helping people see the dangers of Soviet totalitarianism.
Other books were also beneficial by pushing people to fight evil. I'm not aware of 19th and 20th century books that had a major impact in fighting Napoleon or Hitler, but Whittaker Chambers' Witness was useful in helping Americans to understand the evil of Communism. Books by Alexandr Solzhenitsyn such as One Day in the Life of Ivan Denisovich also helped. Hayek's The Road to Serfdom was the forerunner of many books that preserved the West from going further down the socialist path.
Lew Wallace's Ben Hur, a Tale of the Christ, was not great writing, but in the late 19th century it helped lots of people to come to Christ. (Also, the movie's chariot race is still pretty good.) And that leads me to another conclusion: Since the greatest benefit we can have comes through faith in God, I'd put C.S. Lewis books -- especially the Narnia seven and Mere Christianity -- on the list, and then add books by theologians such as Francis Schaeffer, J.I. Packer, and John Piper.