At home I filter the water through the tap with a PUR filter, then that water goes into my Brita tank through another filter. If I'm buying water, my preference is spring water, preferably from the Rocky Mountains.
One thing I noticed during the Fantasy ship inspection was that they served us bottled spring water at lunch. If there is nothing wrong with the ship's water, I wonder why they did that. Have you seen poormom's picture of a filter used to filter ship water? The newer ships are probably better than the older ones.