OS X 10.8 (Mountain Lion) doesn't come with X11 (an X.org window server) installed like previous versions do. But getting Inkscape to run is still very easy.
Download the latest XQuartz and install it.
Next time you run Inkscape, it will ask you, "Where is X11?" It probably won't be in that list, so browse for it in your "Applications" folder, then go inside "Utilities" and choose XQuartz.
Then give it maybe several minutes to run the first time. And there you have it!