The Conventional Wisdom
Beginning brewing books generally say that if your water is good to drink, it's good to brew beer with. While advanced brewers often carefully monitor their water chemistry, most assume that water doesn't make enough of a difference to be important for beginning brewers, or that it only really matters for all-grain brewing.
Water is largest ingredient in beer by volume, and even a casual look at world beer styles will show that certain styles of beer are better suited to certain types of water.
Some kinds of treated water can also add significant off flavors to beer. Most home water softeners work by adding sodium to beer, which will give a beer a salty taste. City water supplies treated with chlorine can give the beer a chlorophenol taste and aroma, which can be described as smelling or tasting like band-aids, plastic, or burning electrical wire. Chloramine, which is replacing chlorine in many water supplies, gives even stronger off flavors and aromas to the finished beer and is harder to remove.
Between water softeners, chlorine, and chloramine, more and more beginning home brewers are starting to fall into the "exception" category, and more are likely to find strange off tastes in their first batch or two if they don't spend some time thinking about their water.
Experiments brewing the same beer with different water chemistry have shown that water treatment affects flavor more than most homebrewers expected, and more and more cities are switching to chloramine-based water treatment. At a minimum, it seems that this kind of general advice should be given with some qualifiers.