I think this is such an important question as water is a vital component in any living being.
It depends on the tap water. As evident from the replies in this thread, not all tap water would be healthy for rabbits. In Canada, municipalities chlorinate the tap water, for example, and this has been linked to bladder cancer in humans. The same goes for bottled water, it can contain chemicals like Monkey stated; in fact, some bottled water is just tap water (Aquafine, for example).
I am on a well that has hard water, so hard that after a month of using it for my rabbits it clogged their drinking bottle sippy spout. Also, too high of a content in certain minerals can encourage the formation of urinary calculi in rabbits but little is known about the safe levels.
Most homes in my area, including myself, are on water distillers, and my rabbits get that in their bottle, but well water in a bowl also. If I were connected to a municipal water system, I’d use a Brita filter for us people and the rabbits.