Your version is 2 years old. We've since had version 3.1, 3.2, and now 4.0 is in Early Adopter mode.
Can you ask to have your version upgraded? Or do a self-install - just download and extract the ZIP file and run the EXE.
If not, you can try running SQL Developer from the bin directory as described here, and the next time it hangs, do a ctrl-break, grab the cmd console text, and send it back here to this thread. I describe this process here http://www.thatjeffsmith.com/archive/2012/06/how-to-collect-debug-info-for-oracle-sql-developer/