We have always packed many bottles of water in our suitcases. I dont see why HAL wouldnt allow you to bring on a case (or 2). The allow cases of beer, as my parents discovered on our last cruise.
NCL Dawn 6/21/06 Bermuda
10/30/08 X Constellation Caribbean
Costa Fortuna 3/08 Eastern Caribbean
Costa Magica 2/07 Western Caribbean
HAL Noordam 11/06 Eastern Caribbean
X Zenith 6/06 Bermuda
HAL Zuiderdam 5/05 Western Caribbean
HAL Maasdam 6/04 Canada/New England
CCL Triumph 12/03 Western Caribbean
CCL Victory 11/02 Eastern Caribbean
Yes, they do allow you to bring bottled water on board, but why would you want to schlepp a couple of cases of water with you when the water on board the ship is just as good, if not better than bottled water. I take a wide mouth empty bottle with me and refill it as I need it.
Kris - don't know when your parents were on HAL that they were allowed to bring on a case of beer, but this is no longer allowed, along with hard liquour. They only allow wine and champagne.