Stating up front that I do not have any concrete facts to base this opinion on, I nonetheless believe (accept as true) that distilling water does something to neutralize the energy capacity of water. There is some good news, some bad news, and some more good news, potentially, in this.
First, if you are not already familiar with Maseru Emoto, you may want to learn a little about this fellow.
http://video.google.com/videoplay?docid=7833758715853620146
He also has his own web site that includes a section written in English.
http://www.hado.net
Emoto has collected some fairly profound & convincing evidence during his studies of water; that water is a very impressionable substance... it may be about the most impressionable substance in this world....outside of people's minds, that is ;).
Water has the capacity to pick up the energy ... or "vibes" or frequency, of many of the things it comes near or in direct contact with... like a smoke stack spewing out pollution, or distribution power wires, or "cell phone" Microwave Towers.... or even the thoughts that a person thinks of inside their head (from a frequency / energy point of view, people and their minds can also be a sort of smokestack, some times). These examples are the first good news, and bad news, the first good news being that distilliing water is sort of like rebooting your computer... or like starting from a clean slate. Your distilled water is now pretty close to being a perfectly clean, blank slate. The next step is to do something, just a little something, to put a positive "charge" on your distilled water. One simple example might be to add some beneficial, trace, organic minerals......or, the next good news ....
based upon Emoto's research, we all have the capacity to impart good thoughts (and not so good thougts) .....energy....vibrations, onto our water (and onto other things animate and non that surround us in our world). So, lets say you distilled some water. Before you drink it, you might add some Sea Salt to it.... and.... or....you might consider the following simple experiment. Close your eyes a moment, focus your thoughts and imagine pleasant, nice thoughts....whatever is required for you to get into that kind of thinking... there are no rules, we all have different ways we make our minds work. Maybe think of something that gives you thoughts of love. While holding this kind of pleasant thought in your mind, reach out your right hand and place it on your jug of distilled water. You can do this silently if you want, or, you can even speak out loud what you are thinking inside your mind.... thank the water, for the life it gives you and the live it gives all the things that in turn help to give you life.
I have not taken any time to try to prove the above experiment, but Emoto has. Like I said, some of his results are fairly convincing. Lets say this idea is bogus and his evidence is all fake.... what will you be losing.... how much skin off your nose, will it be for you to get in the habit of doing this small act? Some people take a different approach. They think of a word that to them is an ideal positive thought, then they write it on a piece of paper, then the turn that paper to face their water jug, and tape it on.......some liquid food for thought :)
PS - on the "leaches mineral" thing, I sorta favor MH's philosophy on this in that, yes, drinking distilled water DOES leach minerals from the body... and this is a good thing! Why? Because it leaches INORGANIC minerals that our body has been doing the thankless job of trying to put out of the way, somewhere, inside it's body, every time we take in INORGANIC minerals.... "dissovled rocks"... like calcium or other hard minerals people like to get from "sweet well water" ;) Rock is rock, doesn't matter if it's been dissolved down to a fine, sandy or gritty silt like size, when this kind of mineral gets inside the body, the only thing the body can do with it is try to place it somewhere out of the way.... like on the inside lining of the arteries.....hmmmm, wonder why they ever came up with the term "hardening of the arteries"?.