I also have a C/C++ background, I'm an intermediate programmer, and I'm currently using those books for learning Java:
Head First Java 2nd Edition ( Covers Java 5.0 )
Big Java 3rd Edition ( Covers Java 5.0 / 6.0 )
( Covers Java from a practical point of view, introductory text to Computer Science. A whole bunch of interesting exercises are included! )
Java How To Program 8th Edition (Early Objects) ( Covers Java 5.0 / 6.0 )
( Covers Java from a practical point of view, introductory text to Computer Science. A whole bunch of interesting exercises are included! )
SCJP Sun Certified Programmer for Java 6 ( Covers Java 6.0 )
( This book is worth reading if you want to get a very thorough understanding of the Java programming language. Sample exams and review questions similar to those on the Sun certification exam are included! )
Worth mentioning is that all these books assume no Java or previous programming experience, except for the Java certification Study Guide, which requires a basic understanding of Java.
Don't forget reading this as well, it might be of interest:
http://www.daniweb.com/forums/thread99132.html
(a whole bunch of Java resources, probably more than I'd ever use)
tux4life
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