Very general rule of thumb: if the water tastes good, brew with it.
Distilled water is fine for extract brewing, but you may find that for certain styles (darker or more bitter ones, in particular), that tap or spring water works better for you.
For all grain brewing, distilled water can be somewhat detrimental if it's not treated with an appropriate amount of minerals for the style. Calcium chloride, magnesium sulfate (epsom salts), calcium carbonate (chalk), hydrous calcium sulfate (gypsum), sodium bicarbonate (baking soda), and sodium chloride (table salt) are all possible additives, depending on the initial water chemistry and desired result. See
www.howtobrew.com, this site's wiki, BYO back issues, or other many other sources for methods of determining the right ways to affect water chemistry for brewing.