Is there a canonical book?
There is the agile manifesto, but for a canonical book?
No. There are lots of books out there.
Specific book recommendations:
Agile Software Development, Principles, Patterns, and Practices by Robert C. Martin
Agile Software Development, Principles, Patterns, and Practices. This is focused on developer practices and coding and is a must read for any developer serious about agile software development. There is also a C# version of the book that he and his son Micah wrote, so if you are a .NET developer, that version might be the one for you.
The art of Agile Development by James Shore
For an insight into overall agile project practices look at The Art of Agile by James Shore & Shane Warden. It's focused on XP practices (but that's really because XP is where all the specific developer practices are defined), but has a big picture focus on how Agile projects work.
A great thing about this book is that James Shore is publishing the whole text on his website for free, so you can try before you buy.
Practices of an Agile Developer: Working in the Real World by Subramaniam and Hunt
Practices of an Agile Developer: Working in the Real World
Scrum and XP from the Trenches by Henrik Kniberg
It's a great book for getting a feel for how an agile team works, and it it's a very quick read (couple of hours). I give it to new staff in my organisation - technical and non-technical - and I've had consistently positive feedback.
Amazon
Extreme Programming Explained by Kent Beck
Probably the oldest book I can remember which helped make Agile principles popular. Agile is fast becoming a buzz word in the world of Tech. I feel Extreme Programming (XP) is a good place to start before the term Agile just seems to lose meaning.
Amazon
Agile Estimating and Planning by Mike Cohn
For "the Agile process" - look to Mike Cohn's "Agile Estimating and Planning" - bearing in mind that it's Scrum-centric.
Cohn covers a lot of the basics as well as some of the things new Scrum teams often struggle with - estimation using Story Points vs. Ideal days, what do do if you fail a story in a sprint, when to re-estimate/size and when not to, etc.
He also goes into some really interesting stuff that's mainly the domain of a Product Owner - things like how to assess and prioritize features, etc.
The Art of Unit Testing by Roy Osherove
Osherove presents a very pragmatic approach to unit testing. Presents a good approach on how to refactor code to become more testable, how to look for seams, etc. It is a .Net centric book, however.
Amazon
The Agile Samurai by Jonathan Rasmusson
Just purchased this myself and found it to be a refreshing look on how to get started with agile.
Amazon
Alistair Cockburns book on his Crystal methodologies is worth while reading - partly because it gives you an alternative the the usual Scrum methods, and partly because he was one of the original guys who came up with Agile in the first place, so I hope he know what he's talking about.
Crystal is an interesting methodology as it scales from small teams to very large ones, he describes the changes required to make agile work in these different environments.
Unsorted books mentioned
Agile Adoption Patterns: A Roadmap to Organizational Success by Amr Elssamadisy
Agile and Iterative Development: A Manager’s Guide by Craig Larman
Agile Estimating and Planning by Mike Cohn
Agile Project Management: Creating Innovative Products by Jim Highsmith
Agile Retrospectives: Making Good Teams Great by Esther Derby and Diana Larsen
Agile Software Development by Alistair Cockburn
Agile Software Development with Scrum by Ken Schwaber and Mike Beedle
Becoming Agile: ...in an imperfect world by Greg Smith and Dr. Ahmed Sidky
The Business Value of Agile Software Methods: Maximizing Roi with Just-In-Time Processes and Documentation by David F. Rico, Hasan H. Sayani, and Saya Sone
Collaboration Explained by Jean Tabaka
Continuous Delivery: Reliable Software Releases through Build, Test, and Deployment Automation by Humble and Farley
Crystal Clear: A Human-Powered Methodology for Small Teams by Alistair Cockburn
Encyclopedia of Software Engineering edited by Phillip A. Laplante
Fearless Change by Linda Rising and Mary Lynn Manns
Growing Object-Oriented Software, Guided by Tests Freeman and Pryce
Innovation Games: Creating Breakthrough Products Through Collaborative Play by Luke Hohmann
Lean Software Development – An Agile Toolkit for Software Development Managers by Mary and Tom Poppendieck
Lean Solutions by Jim Womack and Dan Jones
Lean Thinking by Jim Womack and Dan Jones
Managing Agile Projects by Sanjiv Augustine
Managing the Design Factory by Donald G. Reinertsen
Planning Extreme Programming by Kent Beck and Martin Fowler
Scaling Lean & Agile Development: Thinking and Organizational Tools for Large-Scale Scrum by Craig Larman and Bas Vodde
Scrum Pocket Guide: A Quick Start Guide to Agile Software Development by Peter Saddington
The Software Project Manager's Bridge to Agility by Michele Sliger and Stacia Broderick
Today and Tomorrow by Henry Ford (From 1926)
User Stories Applied by Mike Cohn
Book lists