The main advantage of cumulative voting is that it disperses the
power to elect directors among shareholders, instead of
concentrating the power in the majority shareholder. This can be
helpful in a number of situations, especially when the corporation
is forming and a significant (but not majority) investor wants some
assurance that she will have some power over the board. Another
(possible) advantage (depending on which side you're on), is that
it makes it more difficult to remove directors, because a director
can't be removed under cumulative voting if the votes cast against
removal would have been enough to elect the director. Thus, a
majority vote won't be sufficient to remove a director. This is
another benefit for the minority shareholders, who may be weary
about the majority's control.
