It depends on where you are getting your water from. Here in the Seattle area, we get our water from mountain reservoirs and we have very low mineral content which is good place to start and easy to add the minerals you want. If you live in a place like Arizona, where they mostly pump the water out of underground reservoirs and tastes like crap, you will either want a Reverse Osmosis filter or a go down to Safeway and use the filtering station. Make sure to check your local water report which are usually available from your water supplier.

Reverse Osmosis Filter:

https://www.amazon.com/APEC-5-Stage-Reverse-Drinking-Water/dp/B00I0ZGOZM

I use filtered water (under-counter job with a separate faucet, about $80 from Home Depot), because my public water is disgustingly bleachy. They tell me it's within spec of chlorine PPM, but it's truly awful. Smells like a sanitizing solution.

Filtered Water Kit http://3.bp.blogspot.com/_Yq49vDkFRvI/Rs-kESnYwSI/AAAAAAAAAB0/iw01DxIK1QU/s1600-h/KitchenAfter4.jpg

Well water can have a whole different set of issues. Where I used to live, I had a ton of manganese and iron from a well, so I had to Brita that to make it potable.

If your water doesn't taste "off" you're probably fine, but like Dean said, there are definitely options for playing with water chemistry, especially if you're trying to replicate a regional style.

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.

1. How does it taste? Do I notice anything off about may water? (EG: chloramines, sodium)
2. If my tap water tastes funny, does the flavor carry over to the resultant beer?
3. Am I getting good efficiency and conversion in my mash?

My answers were:

1. Icky. Tastes like salt.
2. Hard to tell.
3. 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.

You can buy a sink filter for under a $100. In the long run it turns out to be cheaper than Brita filters and faucet-mounted filters. So easy to install.

I've always just used my tap water, but I know a guy who takes his carboy to Kroger and just sticks it in the water cooler refilling station, and he says it's pretty cheap.