Books on the Basics of PHP
PHP for the World Wide Web: Visual QuickStart Guide
This visual quick start guide is one of the classics for beginner to intermediate level php programmers. This book takes you from the very basics of PHP5 through to several useable ecommerce examples.
Learning PHP 5
This is O'Reilly's top beginner level book for PHP5.
The PHP Anthology, Volume I: Foundations
This is an excellent problem-solution PHP book. As the name implies, it teaches you foundational PHP concepts that in later learning separate the PHP hobbiest from the PHP professional.
Basics of Using PHP with Databases
PHP and MySQL for Dynamic Web Sites: Visual QuickPro Guide
This visual quick start guide is one of the classics for beginners who want to be intermediate level php programmers and know just enough MySQL to make completely data-driven sites. This is my all-time favorite of the beginner php books.
PHP Essentials
This is the book my peers most recommend to new PHP users. I have not read it, but I have never heard a negative comment about it.
Beginning PHP 5 and MySQL: From Novice to Professional
This is one of the best books for experienced web developers who have limited experience in PHP and MySQL.
PHP in Easy Steps
This is another excellent theory plus practical examples book for PHP beginners.
Core Web Application Development with PHP and MySQL 
This is one of the most popular books for programmers with limited PHP experience who want to take their PHP up to the professional level. It does an excellent job of using practical php examples. This is a great review / follow-up book for the beginner PHP books before moving on to intermediate topics.
Intermediate PHP Books
PHP Hacks : Tips & Tools For Creating Dynamic Websites
This is a new O'Reilly classic. This is a book about PHP optimization, database optimization for PHP, and how to get the most out of your PHP projects. Invaluable PHP tips for those building professional-level web sites.
Advanced PHP for Web Professionals
This book helps improve your overall PHP knowledge. It explores advanced topics not usually covered in beginner books, that programmers would typically have to learn by example and experience.
No Nonsense XML Web Development With PHP
Though more of an XML book than a PHP book, this book is so example-based and practical that my PHP book list would be incomplete without it.
Advanced PHP Books
Essential PHP Security 
This is a good quick review of the basics of PHP security. It is brief and to-the-point, but not an exhaustive source by any means. I recommend it for those who have some intermediate PHP experience and want a concise view of PHP security in their minds.
Pro PHP Security
So you know PHP enough to write a script to do anything you can conceive, but do you know exactly how secure it is? Do you know ALL of your PHP scripts' security strengths and weaknesses? Learn about PHP security and practical solutions to PHP security issues.
PHP Reference Books
PHP Functions Essential Reference
A true classic, this is a nice reference of PHP functions every serious PHP programmer can use (and probably should). This book saves you a lot of time...you know, not 're-inventing the wheel'. This is not for the absolute beginner, but great for everyone who knows how ot use a PHP function.
PHP Phrasebook
Somewhat of a novel reference idea, this is a list of common PHP code phrases that you end up using over and over from one application to the next.
PHP 5 Recipes: A Problem-Solution Approach
A self-styled PHP 'recipe book,' this book is an excellent reference to quickly go into solving problems so that you can concentrate your planning on the flow of the overall script rather than spend a great deal of time implementing individual objects. In other words, lots of samples on how to deal with common tasks you come across in common PHP development.