Are there any games that are open source on JME3? I feel like it would be a great help to me to learn JME if I could play around with a finished product and see how they implement and use some things instead of trying to feel my way through it with the help of the tutorials.
If you didn’t even find the open source games then no, I doubt that 
Do the tutorials, each one is an application.
http://code.google.com/p/rise-of-mutants/
But it’s still in development. But you can learn about entity system and different stuff.