Some very good advice from philosopher Bernhard Nickel at Harvard.  My only small caveat is this:  while I agree with Professor Nickel that the writing sample need not be in one's primary area, if it is too far afield of anything the department does, that will not work out well (e.g., don't submit a paper on Heidegger when applying to MIT).  Comments are open if others have thoughts about Professor Nickel's advice.   Signed comments (full name and full email address, the latter of which will not appear) will be preferred.