Distilled water tastes like shit, despite what water distiller salesmen would tell you. The only thing it's good for is topping off a radiator.

I have at least a dozen conspiracies to believe in before saying that in general, tap water is bad for you. There are many places in the world I wouldn't drink tap water, but where I live, (Ontario Canada) I have no problems with the municipal supply. I drink much more water than most people I know - seeing as I don't drink any type of sodas. Apart from water there's wine and some beer every now and then. But since those aren't daily, water is "it" over 90% of the time.

Right now we use a Brita filter jug, but that's mostly as a convenient vessel to hold the water in the fridge rather than for filtration purposes. When I get the new fridge I'll be using its built-in filter and don't plan to install anything under the sink nor whole-home.

If you're concerned about the purity of your water you should be very concerned about filtering whole-home because you also absorb a lot of contaminants through your skin when in the shower and the bath.

I don't call it tasteless. Having nothing in my mouth is lack of taste. When I put something in it and can perceive a difference, that's a taste. Municipal water here is not heavily chlorinated, so I don't have a problem when I have to drink some unfiltered. I've got extremely sensitive taste buds and sense of smell, so if there's even the slightest detectable parameter off in water, I'll be the one to notice it.

I'm so glad our new house won't be using copper pipes, because I've been able to taste that every now and then as well.