The water from the faucet in your cabin is the same water used by the various chefs and cooks aboard a ship to prepare your meals and wash your dishes. It is perfectly safe. I made drinking water for years in the U.S. Navy, distilling seawater and purifying it into potable water. People seem to think if water is put in a pretty bottle it "must" be better. This isn't really true.
I always ask for ship's water in the dining room, and use it to take my meds in the cabin.
I've always drunk ships water, save my money for something more exciting than water!!! To me it tastes just fine. I usually start the cruise with a bottle, then fill it up and chill it in the fridge for shore excursions. That's the only thing--tap water is never cold, at best lukewarm. They have ice for you, you can get it at bars, dining areas, buffet or room service.
Tap water is OK, but I like to use the bucket of ice to drink or fill my bottle because it is refreshingly cold all the time as it melts. I ask for 2 buckets every evening in my room.
Pacific Princess Sept/01 - Family in Pacific Northwest
RCI Radiance Of The Seas April/06 - 25th Annversary in Panama Canal
HA Volendam Sept/06 - Dad's Surprise in Alaska
Crown Princess April/07 - Fun In The Sun in Eastern Caribbean
RCI Brilliance Of The Seas March/08 - Here We Go Again
RCI Vision Of The Seas Dec/08 - Joining Sis On Her Redneck Honeymoon in Mexico
I liked Dave56's response. I have cruised 20 some times on six different lines. They make the ice with the same water you drink and I have used a lot of ice. You can take bottled water on board for a lot less money that they charge. I am still trying to figure out the deal with bottled water. Most of it comes from wells and is no different that the water from the tap.
Regal Princess 1996
Sun Princess 1998
Grand Princess 2000
Ocean Princess 2001
Golden Princess 2004
Caribbeean Princess 2004
Caribbean Princess 2006