Things that have not be put elsewhere.
Remote logging
Program which can be used non-interactively to be used in web applications or something else
See also this
Similarly to the above, some functionalities of yorick (e.g. writing a mpeg movie using yorick-mpeg) require the openning of an X window. When I want to do it non-interactively, I use a VNC server instead of a "real" X11 display. Other "dummy" X11 servers suitable for this sort of tricks may exist. ThibautPaumard.