I have heard that the problem with distilled water is that it pulls out minerals, including trace minerals that are not available without a prescription, like lithium.
Most people get most of their lithium from the water that they drink. Vegetables are an additional source, but water is the major source. In other words, virtually everyone reading this post has lithium in their bodies, and needs to in order to be happy and comfortable. (People think that lithium is only for manic depressives, but this isn't true. Lithium plays many roles in our bodies.)
Lithium is just one example. Long story short, according to my research, in order to stay healthy we should drink water that comes from the ground and isn't distilled.