So far I'm the only dissenter here. I DO use tap water BUT I run it through a poly filter and, the last week, a nitrate sponge because I'm having a hair algae problem, despite the massive amounts of caulerpa in my tank. However, I don't always recommend this. My water comes from a limestone aquifer and is VERY high in calcium and carbonates, which keep my calcium levels and alkalinity in tip-top shape. Unfortunately, there are some (0.1 ppm) phosphates and nitrates (1 ppm) in my tap water, hence I use the filters.
The use of tap water in no way has caused any problems for my "delicate" corals. They're growing at a fast and furious rate, some even overcoming recession problems in tanks with too little light. I think so long as we provide our corals with a ball park temp and salinity, good calcium and alkalinity, and excellent light, they're very hard animals!
The bottom line before you use tap water, know what's in it! Your Public Utilities Commision should have that information readily available. Good luck!