I am a big fan of Fawn Brodie's No Man Knows My History, a historically accurate and extremely readable biography of Joseph Smith. There was an interesting discussion of this book on a Mormon-themed blog recently.
The interesting thing about this book is that the Church has spent two generations painting it as the personal vendetta of an apostate bent on destroying the Kingdom. The church's own apologist-in-chief Hugh Nibley did a particularly unscrupulous (and embarrassing) hatchet job on it and this has been continued by the FAIR and FARMS crowd. However, when Richard Bushman, a faithful LDS historian, finally got around to writing Rough Stone Rolling, the closest thing there is to an uncontested Joseph Smith biography, he borrowed so heavily from Brodie that he effectively vindicated her. The Church does not contest Bushman, but his book contains the same facts as Brodie! (In fact, I argue that it adds so little, it should not have been written.) The only difference is that Bushman changes the tone and paints Joseph Smith as more of a passive observer rather than a charismatic leader. The blog post I mentioned earlier has an interesting comparison between Brodie's Joseph Smith and Bushman's. For my money, Brodie's book is much, much better written. She has a gift for narrative that Bushman lacks. And after all those years of Brodie-hating, the Church has effectively granted all her points. I guess it's too much to expect an apology. In any case, I can't recommend NMKMH too highly.
To fill in the gaps left by Brodie, I also like Mormon Enigma: Emma Hale Smith by Newell and Avery. Emma Smith's story is fascinating and puts a lot of the other material in context. Official Mormon history pretty much leaves women out. If your only exposure to LDS history is the correlated version you read in the lesson manuals, you really owe it to yourself to read these two books.
One more book I want to mention is Roots of Modern Mormonism by Mark P. Leone (Harvard Univ Press, 1979). This very readable book shows how Mormonism went from an interesting and freewheeling band of outsiders to end up as the stodgiest kind of establishment religion imaginable. Leone shows how Utah's statehood and its aftermath changed everything. It was a remarkable transformation. If you read Brodie and wonder what ever happened to that church, Leone's book tells you.
(I also want to plug the recent podcast about correlation, described here.)