I would advise you go through some of the Free / Open Source Software sites that host the projects and start filtering your searches for Java projects with a high number of users / downloads, as they tend to be fairly mature and will allow you to start looking through them.
My main recommendation is Arianne (http://arianne.sourceforge.net/). It's won several awards and is quite professional. There are only two listed developers, and they seem quite friendly. Plus, it's a multi-tier video game engine, so there's plenty of fun you could get out of working on it.
Otherwise, check-out java.net, kenai.com, and sourceforge.net for more possibilities.
If you want an early project with potential, there are plenty, but it can often be the luck of the drawer with those.