I have a 4 stage reverse-osmosis filtering machine that makes 2.2 gallons of laboratory grade II (very pure) water in about an hour. Total dissolved solids measured with a TDS meter is 0 ppm. TDS measures around 400 ppm with plain tap water. (a measure over 500 ppm exceeds the EPA maximum recommendation) There is absolutely no smell or taste with the purified water from my machine. Love it. It's the bee's knees!
My wife goes to visit her mother in the midwest and can immediately taste a difference with their tap water. She's freaked out by the weird tasting tap water and must drink bottled water there.