Distilled water is the best water to be drinking because it is a thirsty water, when you drink the distilled water it pulls the extra fats and minerals that your body doesn't need out of you bloodstream where they just clog and slow down your body systems and passes them through your urine. You get all the good vitamins and minerals that your body needs, and can handle through your fruits and veggies. Not through water, if you get them through water then most pass right through your system, you might as well be drinking distilled water if they are now absorbed into your body like they will/should (if your healthy) through fruits and veggies.
When you have too much of a certain mineral or vitamin, your body stores it in deposits throughout your body and blood stream, these are very unhealthy and can hurt.(kidney stones) When you drink distilled water, the water pulls the extra's out of your system and gets rid of them. NO other water will do this.
I have been drinking distilled water only since I have been married (I wasn't a huge health fan before) and I have noticed a difference, not a big one, but I have noticed one. Also I am able to drink more distilled water in a day then other waters. Spring water I can only drink about 16oz before I can't stand "the taste, or lack of taste" my mouth tells me to please drink something else! With distilled water I only get that if I drink a huge amount in a short amount of time.