I have next to no programming experience, and absolutely none with Java, so I'm looking for some good online tutorials/primers. Please point me to good ones for beginners like me. Thanks.
Straight to the source: http://java.sun.com/docs/books/tutorial/
Video Tutorials: http://www.javaomatic.com/
These questions should help you out.
http://stackoverflow.com/questions/167179/java-tutorial
http://stackoverflow.com/questions/86103/books-and-tutorials-for-beginners-in-java-and-php
http://stackoverflow.com/questions/721604/programming-with-java-for-beginners
Also, as you gain some java experience, you will almost certainly find yourself looking to use the APIs - http://java.sun.com/reference/api/
APIs give the documentation and examples on the classes/objects available for use in a particular Java release. You will find a lot of answers there moving forward. Good luck.
A video from Stanford - good presenter makes it easy to watch and pretty fair examples too http://www.youtube.com/watch?v=KkMDCCdjyW8