Java a Beginner's Guide is an excellent book. The authors site is http://herbschildt.com/. amazon.com always has a great price. 4th Edition is the current and the next version updated for Java 7 will be released I think in July this year.
The book is not just an excellent read, but the author has substantial experience in C based languages. He has several books on other languages and every book follows the exact same guidelines including most of the same exercises. So if you later switch from Java to C# to C or to C++, if you get the other books, it will be easy to remember the structure, which will allow you to transition between the languages. In my opinion, some of the best books ever written. Also, the books are always available as a Beginner's Guide, or a Complete Reference. Personally, I suggest the Beginner's Guide, but if you follow up with one of the Complete References, you will notice it is almost the same with a great deal of more detail. Again, the entire idea I believe in his series of books, is to keep everything consistent and transferable between languages. If you choose to switch to C++ when you discover it might be necessary for a specific game, the transition will be smooth. You will be able to reuse just about everything you learned in Java and vice versa. I highly recommend you give Java A Beginner's Guide 4th Edition a try, even if you are a veteran programmer. Clear and concise book. Good luck.