In Forbidden Island, can a Navigator move an Explorer diagonally?
Good question!  And fortunately for you, the answer is "yes", as per these clarifications
by Matt Leacock, the designer of the game:


  The Navigator can move the Diver up to 2 adjacent tiles. The first
  tile may be missing. The second tile may not be missing because the
  Diver must end her turn on a tile.
  
  When the Navigator moves the Explorer to adjacent spaces, he may move
  him diagonally.
  
  The Navigator moves the Pilot to adjacent spaces like any other
  adventurer. (The Pilot can't take advantage of his special ability
  when the Navigator moves him.)