The Java Series
The series as a whole works well. As the marketing material says, it represents the definitive source of Java information. I haven't found any books outside this series that add much in terms of raw information.
Although these books are well-produced and provide valuable information, I can't recommend that everyone go buy them. If you are a student with a limited budget, as I am, you might want to look into something like Java in a Nutshell (O'Reilly and Associates). It provides a tutorial for C programmers who are trying to learn Java and also has an good API reference. Other places to find cheap information on Java include the SSC API reference cards and JavaSoft's web page.
On the other hand, if the price of a $30-$40 reference book doesn't make a dent in your wallet and you need to have the official source of Java information, all five of these books are very good deals.
One final consideration—a new version of the Java Development Kit has just been released. It has introduced numerous changes and additions to the class library. Therefore, I suggest waiting to buy an API reference until it includes JDK 1.1 information.