Anybody know of a good open source project I could work on to build up my experience? I've got the BS degree in Computer Science, but the I keep getting shot down for Java programmer jobs because of lack of experience I'd like to change that. I'd appreciate any helpful advice.
Like Jeanne said, "best" is what you feel is best.
Head over to http://sourceforge.net/ You can search for projects (I searched for games and it gave me 21,178 hits). Read the description and find out if the project creators are open for contributions.