The River of Lost Footsteps by Thant Myint-U. Easily the most accessible history of Myanmar available. Read it before you go and you will marvel at how the once great and rich cities (like Martaban, Syriam, and Mrauk-U) have been transformed into the dingy and smoky villages of today. (ISBN 0374163421)
From the Land of the Green Ghosts by Pascal Khoo Thwe. A Cambridge-educated writer who gives a very touching account of his growing up as a Paduang-Hilltribe-Guyand in the difficult political environment before turning into a rebel himself. (ISBN 0 00 711682 9)
The Glass Palace by Amitav Ghosh. A novel that spans a century, from British conquest to the modern day. A compelling account of how a family adapted to the changing times; provides much insight into Burmese culture.
Burmese Days by George Orwell. An absolute must read, classic novel about Burma.