Learning Java 3rd Edition
Amazon.com: Learning Java
Amazon.co.uk: Learning Java
Amazon.com: Effective Java
Amazon.co.uk: Effective Java
Joshua Bloch is a Java genius. A 2nd edition is out soon according to Amazon.com
Recommendations (Updated for Java 5):
Thinking in Java (4th Edition)
Amazon.com: Java Puzzlers
Amazon.com: Java Precisely, 2nd Edition
Java Cookbook , Second Edition
I have the first edition which is excellent, but the 2nd edition is updated for Java 5 so that's on the list to purchase.
Head First Java , Second Edition
Java Network Programming , Third Edition
Head First Design Patterns
Java 5.0 Tiger: A Developer's Notebook
Filthy Rich Clients: Developing Animated and Graphical Effects for Desktop Java™ Applications
Amazon.com: Pragmatic Unit Testing in Java with JUnit
Amazon.com: Java How to Program (7th Edition)
Amazon.com: Java Concurrency in Practice