When we buy bottled water, we create incentive for corporations to make plastic bottles; rob people of their water rights; ship large quantities of water all over the world, with the fuel consumption that entails; and paint bottled water as a status symbol and "healthy lifestyle" marker (which is, ironically, quite unsustainable).
When we drink tap water, we create incentive for the maintenance of infrastructure that provides safe drinking water to populations as cheaply as possible.
In this I see parallels to the "industrial/away food" vs. "local food" situation.
Bottled water sends profits to corporations to support an unsustainable, economically unjust product. Tap water creates local infrastructure that is valuable now, but will become even more valuable if there is a discontinuity in our transportation system.
Bottled water, like factory organic food, may have fewer impurities in it than tap water—or it may not. It is important to consider, however, that bottled water has generally sat for months or longer in its bottle, almost always plastic, often in conditions of extreme heat. Is this safe? Unclear.
Bottled water is a luxury and convenience item, and ought to be viewed as such. There are times when it is very nice to have.
But for everyday use, tap water fills the bill. Filtered tap water can be at least as pure as any bottled water, for less money, and with less waste.
I've come across some restaurants, yoga studios, etc. that eschew bottled water in favor of filtered water, even though by doing this they are giving some profits.
I hope this trend continues.