This week's giveaway is in the EJB and other Java EE Technologies forum. We're giving away four copies of EJB 3 in Action and have Debu Panda, Reza Rahman, Ryan Cuprak, and Michael Remijan on-line! See this thread for details.
I would suggest to use J2ME: The Complete Reference as a starting book.
Be aware though that -according to its Amazon reviews- this book covers MIDP but not CDC (which is an important part of JME). Also note that the book is from 2003, so it doesn't cover the current MIDP 3.0 version (although, in fairness, that isn't used much out in the wild). That kind of reflects the fact that -IMO- JME is on a downward path, not an upward path. The only "hot" smartphone that uses JME at all is the BlackBerry, and even that needs all kinds of non-JME, BB-only APIs to do some of the advanced stuff.
So, if you want to use the Java language to develop for mobile devices, Android might be a better choice (depending on the market you're after).
Ping & DNS - updated with new look and Ping home screen widget