Everyone has a different choice. I like the books endorsed by Sun. Core JAVA 2 Vols I and II. My feeling is they were written by Sun who developed JAVA and also written by someone who helped develop the tests. Horstmann & Cornell. Vol I Fundamentals, Vol II Advanced Features.
Also the book written by someone here on this site gets a lot of good press. By someone K & B. I am sure there must be an ad someplace. I think they sponsor this website or something like that. I may get a copy and read it before I test.