While it's not a case study on how to build a forum, the chapter that I wrote for
Professional Java Servlets uses a very simple discussion forum to demonstrate the principles around web application design using
patterns, model 1 and model 2 architectures.
Wrox have kindly made available a couple of
sample chapters from the book, one of which is mine.
Since the purpose of the chapter is to outline good design, I wouldn't necessarily recommend that the code is used in a production environment as-is, but it might provide you with some ideas.
Alternatively, and if you are looking for a product, check out something like Jive which is a discussion forum written in Java.
Cheers
Simon