Hmmmm... if I turn off my WIFI I get:
In[3]:= Run["ping Google.com"]
Out[3]= 17408
But if I have it on, when I execute
Run["ping Google.com"]
it does not terminate and locks up the Kernel. Usually when one does a ping in a terminal it is a process that continues until one executes a control-c. I had to Kill my Mathematica to continue... the usual attempt to abort does not work in this case. So perhaps this is not quite a usable. ;-)