There are many open-source projects that are written in Java- such as Google's Android Mobile Platform.
If you've just started learning Java and would like to improve your Java skills here some useful tutorials and links.
Sun's Java resources.
The best place to learn about Java and Java APIs is of course the Sun website.This is the "official" Java learning material.
JavaRanch is a great place for Java newbies to get their doubts cleared.It was started by Katy Sierra - author of many "Head-First Series" books.
Learning Java-Exercises/Mini projects
Its always good to learn by doing.These links contain very simple - easy to implement projects, that will help you explore the Java language.
Other useful websites/articles
JavaWorld is useful for an in-depth analysis on many Java programming concepts and APIs
Java2s is good for downloading jar files.Also has some useful how-tos and tips.