I picked up No Man Knows My History, first, because I wanted to learn more about Mormon history; and second, because Brodie is a large source of information for many other books on Mormonism.
Fawn M. Brodie's writing style is dry and academic. Nearly every page features a citation in the footnotes. Most of her sources, in fact, come from church documents like History of the Church, or the published journals and letters of the characters themselves. Joseph Smith founded a religion in the time of the printing press, and Brodie built a book on the evidence of the printers.
She approaches Joseph Smith as a man, rather than the perfect mouthpiece of God as many Mormons view him. In some ways, this is an unfair approach. Abraham (of the Biblical Old Testament) looks like a crazy person if the reader doesn't accept that Abraham hears the voice of God and acts on those words. On the other hand, Joseph Smith wasn't a perfect mouthpiece; he wasn't God. Brodie outlines mistakes and failures as well as successes, and this makes Smith look a little more human that Mormons wish. Appearing human shouldn't be a bad thing. Paul (of the New Testament) knew he was a retched sinner, but he's revered almost next to Jesus in the Christian faith (but not quite).
Fawn M. Brodie's No Man Knows My History: The Life of Joseph Smith is an fascinating book. Her work, no matter how controversial, is worth consideration. Although it crashes against the re-crafted history of the Mormon church, I recommend it to anybody interested in LDS history--especially present members of the LDS church, apologists working with Mormons, or anybody generally interested in the Church of Jesus Christ of Latter-day Saints and its history.
*I have no material connection to this book.