Um, there's no 1 book anymore. Scholarly work on Japan and East Asia in general is putting out a lot of works recently.

If this was the 1960s then I would say George Sansom's a History of Japan would be your best books to get an overview of Japanese history, it's still very good, but the series has been outdated.

If this was the 1990s then I would suggest John Dower's Japanese History and Culture from Ancient to Modern Times: Seven Basic Bibliographies, as a wonderful resource guide, but this book is also getting outdated.

For more recent books (after 2001AD), there's lots. Here's a few college textbooks.

All of history: Conrad Schirokauer's A Brief History of Japanese Civilization

Collection of essays on Premodern Japan: Karl Friday's Japan Emerging

Textbook for modern Japan: Andrew Gordon's A Modern History of Japan: From Tokugawa Times to the Present

Source book for all of Japanese history: Wm Theodore de Bary and Donald Keene's Sources of Japanese Tradition, 2nd edition (2nd vol is huge)

I'm sure there's more, so I hope other people will add to this list.

Edit: Doh, I just remembered that we have this link http://www.reddit.com/r/AskHistorians/wiki/books/eastasia#wiki_japan