There are two issues here: purity and taste. The purist water tastes horrible -- it is flat, lifeless, still. The only way to have great tasting water is to give up a little purity. The objective is that the impurities are "good impurities" -- specifically healthy minerals. They're good for you and make the water taste great.
Many water supplies have water filled with healthy minerals, and those minerals are still there even after whatever they do to treat the water. Chemical treatment leaves the minerals intact, but may lend some of their own flavor to the water, which would be bad.
Water purified by reverse osmosis is very pure, and the better the purifier is, the worse (the more "flat") the purified water tastes. Filtered water is not quite so bad; generally, home filters just remove larger impurities. Of course, that raises concerns about its purity, in some areas. Bottled drinking water actually comes in two varieites: Water purified by reverse osmosis (or some other, similar method), but remineralized (they deliberately put in specific impurities to make the water taste better), and natural spring water.
For me, on average, I don't see a difference between the two types of botteled drinking water, even though they're radically different products. I find them far better, though, than what we can get out of our sinks here in Burlington, filtered or unfiltered. We have unremineralized reverse osmosis at work, and I'd rather drink bleach.