 There are many references to the number "13" throughout the movie.  The room is numbered "1408", add each number together equals 13. The  room is on the 14th floor, and the Hotel skips the 13th floor, so  the room is technically on the 13th floor. The rooms key lock also  has "6214" etched into it, which adds up to 13. And the first death  was in the year 1912, which adds to 13.