I'd like to be the first one to participates.
During my study of Java SE i believe we got two main projects -most likely named as homework- i think they were very good to get command of certain points.
The first was Complex Class ; this class was supposed to do every operation on complex numbers , it helps us to make dealing classes very simple.
The Second and higher in level was Logic Simulator "another option for non engineering purpose Paint",this prog. was supposed to suppot all logic gates and perform logic operations on them and build GUI for the prog. and add anything else you want -yes an open project-it helps us to be good at GUI and also higher level of interconnecting classes and inheritance.