Personally, I would just bring my own water bottle(s) and fill them from the tap. The price of on board bottled water and the hassle of carrying on bottled water isn't worth the chance that there may be a slight issue with any ship's water. Note: None of the issues mean that water is not potable. The cruise lines check the water on a daily basis and the water itself is comes from distillation or reverse osmosis processing of sea water.
"Usually" the water is as good or better than any public water source with no off taste or discoloration. However, it is possible that there is a chance there will be some taste or discoloration in the water. This comes from the pipes getting older or because of maintenance.
I never had a water problem until the last few cruises. Carnival Pride had an off flavor to the water on both my 11/08 cruise and 5/09 cruise. The Statendam had some discoloration in 2006 and Radiance of the Seas had a few episodes of very brown water that lasted a few seconds. They were working on the plumbing on Radiance.
Because of these experiences I no longer make the blanket statement that "all" cruise water is as good or better than bottled water.