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. "Finding George Orwell in Burma" by Emma Larkin. An interesting book on the author's travel through Burma that uses Orwell's experience as a template.