What is more appropriate — "hanged" or "hung"?

Hanged has the specific meaning of execution by hanging, with a rope, "until dead." From NOAD:

2 ( past hanged ) [ trans. ] kill (someone) by tying a rope attached from above around the neck and removing the support from beneath (used as a form of capital punishment) : he was hanged for murder | she hanged herself in her cell

For all other purposes, use hung.

In this context only 'hangs' seems to be appropriate as this is the action that the software performs itself -- it's not being hung/hanged by any external force. Also, as chaos mentioned, it sounds awkward.

In fact, if I received a report saying 'When we execute this command, software X gets hung' I'd ask for clarification -- what hung it? This form may suggest that there's another reason for it, not mentioned in the report.

I would use "hangs". "Gets hanged" is inappropriate and awkward, saying that the software has been executed by hanging, and "gets hung" invokes a slang expression regarding the size of sexual anatomy. ("Gets hung up" would avoid this, but "hangs" is still better.)

Fun fact: being sentenced to "death by hanging" and "to be hung by the neck until dead" denote different forms of execution. "Death by hanging" means to have the knot of the noose placed to the side of one's neck so that the neck is hopefully broken by the drop; being "hung by the neck until dead" means to have the knot placed in back of the neck so that one survives the drop and dies slowly of asphyxiation.