I recommend The Core Java pair of books by Cay Horstmann, supplemented by Effective Java by Bloch. Those are probably the two most authoritative sources on Java out there, and both highly readable.
I heard not so good things about Herb Schildt's book.
I second this recommendation! I read Horstmann's books recently and they were excellent. He really puts things in context – any time I was thinking "WTF? Why would they do things this way?" he had an explanation coming up (or in some cases an acknowledgment that it is indeed a WTF).
Horstmann was one of my favorite teachers at San Jose State. He's a really sharp guy, and very enthusiastic teacher. I had him for a programming languages class and we dove into the various implementations of closures that were to be added to Java. We compared these to Scala and some other languages. Really fun diving in with his explanations along the way.
I heard not so good things about Herb Schildt's book.