Are you talking about individual players?
If so, I don't know, but as of 2004, there were two players who had played their entire careers without a goal (and had played a substantial number of games).
Dallas Eakins played 120 games without ever scoring a goal.
But the winner of this one was Steve Halko, who played 155 games without scoring a goal.
Now, this is only for players who never scored a goal, not scoring droughts, but it's something.