It depends a lot on where you live.
I used to live in Olympia, Washington. The tap water came from 600 foot deep artesian wells. I spent some time in Austin and the tap water literally made me vomit if I drank it on an empty stomach.
I also brew beer. I decided to check the Water Quality Analysis published by the City of Galveston, Texas when I started brewing beer. I found out that there are trace amounts of benzene, toluene, and xylene (paint thinner) in the tap water. They are below EPA levels, of course. When I asked the City of Olympia why there wasn’t any information on benzene, toluene, and xylene in their report (for comparison) they replied that they don’t have these things in their water.
That’s when I realized that Galveston’s water is fed by an open reservoir in Texas City, where some 30% of the nation’s oil is refined and where BP recently had a refinery explode.
In Taiwan, almost nobody drinks the tap water. Everyone buys bottled water and drinks it. They all told me that the tap water was not safe to drink.
Also, take into consideration your pipes. If you live in an old house, the pipes are likely very old and dirty, maybe rusty, certainly putrid. All your water is coming through those. I have had water from old pipes that gave me a headache before.
Because of all these reasons, I buy pre-filtered water. Usually Ozarka brand spring water. I used to drink Distilled water, but I don’t anymore because I found it made me feel weak. People claim that tap water is perfectly safe, of course, and I believe them. But I prefer the flavor and scent of the water I buy.
My girlfriend recently bought a Brita pitcher. It makes vast improvements to the tap water, but I can still detect a hint of something in it that I don’t like. I’ll cook with it and make tea with it, but for straight drinking I still prefer pre-filtered water.
Good luck!