I've been working on Google Apps and the Google Apps APIs since I joined Google less than two years ago and I recently got a review copy of one of the books available on this topic.
The book is called "Google Apps : Mastering Integration and Customization" and is published by Packt Publishing. It was only released a few months ago but it is actually the English version of a French book that came out one year ago. This can be noticed in some chapters that were not recently updated and, as you know, in a tech world that changes so quickly, it is pretty easy to stay a little behind. Also, a few screenshots are in French, but that is only minor nuisance.
The book is split into four parts, targeted to different audiences: senior executives, end users, system administrators and project managers respectively. Being a developer myself, I wish a bigger section for software developers was included, but the book is definitely not targeted at programmers.
The best audience for the book is composed of technical managers and executives that want to understand more about the cloud computing paradigm and its advantages in order to offer it or consider it for their internal IT department.
Part 1 (chapters 1-2) describes the basics of cloud computing and Google Apps in particular, and devotes a chapter to the reasons why Google can be trusted for what concerns data protection, reliability, and security in general. Chapter 2 is available for free and can be downloaded from the publisher's website.
Part 2 (chapters 3-6) covers the various Google Apps services, including Gmail, Calendar, Docs and Sites. Not all available services are described, but the Google Apps suite continues growing almost every day and it would be very hard to always stay on top of the news. Chapter 5 focuses on security features (e.g. Postini), while chapter 6 explores some of the possibilities for third-party developers to extend Google Apps, including the Google Apps Marketplace and App Engine for Business.
The third section of the book (chapters 7-11) explains how to manage a Google Apps domain and includes my personal favorite parts of the whole book, chapter 8. This chapter is devoted to setting up a Single Sign-On solution compatible with Google Apps, one of the most challenging tasks that many system administrators have to face when migrating to the cloud. I didn't find the rest of this section as interesting as chapter 8, as it covers the API, Chrome/ChromeOS and Android, and presents some Marketplace applications, but the authors didn't go deeper into the details (I guess for obvious space constraints).
The final part of the book (chapter 12-14) is devoted to implementing a proper migration strategy in order to jump into Google Apps. The three chapters respectively discuss the solution design, how to start with a pilot project and, eventually, how to perform the actual migration, including specific solutions for those coming from Microsoft Exchange or Lotus Notes.
In general, I'd recommend this book to those matching the target audience. If you are a system administrator or a project manager and don't know yet what this "cloud computing" thing is and why everyone is "moving to the cloud", this book can answer many of your questions. If you are a developer willing to integrate his application with Google Apps, this is probably not the best reference material you can get, but I'd strongly recommend you to get in touch with people in my team at Google (the Developer Relations team) and reach out to us on our forums.