Most tap water (in America) is good for brewing
I recommend removing (filtering) or adding things to your water only if you have a problem with it. (Or want to create a beer with a historic profile, like Burton on Trent, Pilsen, or Dublin.)
Your water influences a few things in the brewing process, namely the mash and the overall product. When evaluating which water to use, ask yourself some questions.
- How does it taste? Do I notice anything off about may water? (EG: chloramines, sodium)
- If my tap water tastes funny, does the flavor carry over to the resultant beer?
- Am I getting good efficiency and conversion in my mash?
My answers were:
- Icky. Tastes like salt.
- Hard to tell.
- No, my efficiency is crap
Turns out the water in my area is crap for brewing.
Water-influenced flavor problems
Try purchasing spring water or filtering your water. If you mash or mini-mash do not use distilled or reverse-osmosis water. I built this cheap filter that should be good for about 770 ten-gallon batches.

Mash problems
Poor efficiency could be caused by water chemistry. The mash needs to reach a low pH for optimal enzyme activity. Minerals in the water may prevent it from reaching 5.0-5.6 pH and filtering generally does not help with this. Obtain your local water report. It should be available on your water company's web site, or search "water report" and the name of your town/city and state.
Some qualities, like too much of a problematic mineral, can be solved by diluting with RO water. In rare occasions, like mine, you have to build your water from scratch. This is a good motivator to learn the necessary water chemistry related to brewing. It's beyond the scope of this question, so I won't go into it here.