Here's what I plan to do as an introduction to Java:
First, we'll run through some simple, text-base applications. This will introduce the basic structures and data types in the language, and will serve to introduce object-oriented programming. Object orientation is where much of the magic and power comes from in Java. Object oriented programming can be a little weird at first.
As quickly as possible, we'll get into the graphics and networking capabilities of Java. If you have little programming experience, it will be difficult to appreciate just how easy Java makes this. In fact, it is nothing short of astounding what you can do with just a little practice.
We'll work through a couple of games that I have put together as examples- Craps and Go Fish. We will create classes of object that will encapsulate the behavior of dice and cards. With these classes, we'll construct our games. Then, with these same classes, you will be able to write your own examples, like, for instance, Yahtzee and Poker, or whatever sounds interesting. I'll post suggested approaches, and answer questions if people send me them.
These examples will teach you a lot about the Java language. Enough, in fact, that you will be able to use it to write programs to do things that you want done. Games are non-trivial, fun ways of learning programming languages.
Then, if anyone is actually paying any attention, and I am not just farting into the great Chinook, we can pick a scientific application and write some software to achieve some goal. If not, I'll just figure out something cool to do, and post that.