I used to drink distilled water on a regular basis.
http://www.nutriscience.com/nutrition/Hydrate-Water-Health.htm
I am a big fan of Dr. Michael Colgan and his books, which make 100% sense to me because they are not only theory, but everything is backed up in practice with athletes that are coached at his colgan institute and their experiences. Here is the way he thinks:
Distilled water, with about 1-14 parts per million contaminants, is rated by the National Science Foundation as the purest source of water. This is the same water you put in your iron and your car battery! It's funny that distilled water has been around forever and is the cheapest, yet most of you do not drink it. In fact, distilled water is all anti-aging specialist Dr Michael Colgan (of the Colgan Institute) will drink. I have trained many athletes that drink one to two gallons of distilled water every day.
I am commonly asked about the mineral content of distilled water. It is a commonly held belief that distilled water leeches minerals from your bones and teeth because of osmotic pressure. This is a myth made up by smart marketers of spring and mineral water to increase sales! Any basic college text will reassure you that the human system does not work that way. If it did, your cells would be at the mercy of all the varying osmotic gradients created in your gut by every meal you eat. Remember too that the purpose of drinking water is hydration, not to supply minerals. You obtain minerals from food and supplementation. Distilled water is absolutely pure and clean and is the best source of water you can put into your body.
A lot has to do with the origin of the minerals. Water contains inorganic minerals that come from rocks that the water comes in contact with. Our bodies, however, cannot use these inorganic minerals. It needs organic minerals, like the ones ocurring in plants and/or meat. These are the ones absorbed by the body and used by our cells. In his book "Optimum Sports Nutrition" he gives a very good explanation of how it is not chemically possible for water to have an isolated effect in our bodies, because water is not by itself in it. The leaching minerals belief comes from experiments done "outside" of the body.
For more information, check also this article: http://www.academyofnaturalhealing.com/articles/distill.html
I do however have concerns with the plastic in which the distilled water is normally sold. I do think that it's is not prepared to package things for human consumption (normally distilled water is sold for car batteries and irons) and might contain carcinogens and who knows what other contaminants, so I was more worried about that, than the water itself and therefore stopped drinking it. I would however, if I could afford it, get a home water distiller device and would drink home distilled water with absolutely no worries.
Just my 2 cents
Vivalavida