Inspired by this question. How do I test my water?
A city water report is the first place to look, but given where your city gets it's water, the values can fluctuate pretty significantly. For example, my city gets water from a few sources; sometimes they'll mix in well water, and thus the water has higher hardness, or they might be taking surface water shortly after a fresh rain.
The question to also ask is "why" should you test your water. To answer that, a good starting point are sections 15.0 though 15.4 in Palmer's How to Brew: http://www.howtobrew.com/section3/chapter15-1.html
Water chemistry does have a significant affect on beer flavor. Often water chemistry is the last bit of tweaking needed to make a good beer great. Having said that, it's also an easy way to muck up a beer. Water chemistry (aside from proper filtration) should be your last concern in making beer. Sanitation, yeast handling, temperature control, recipe formulation and brewing process should all come first.
If you have city water, they usually sent out a water profile a couple of times a year. It will be an average of the whole city, but it'll give you a general idea of what you're dealing with.
You can also send your water away to a lab to get tested. I've never bothered, so you'll need to find a reputable lab.
I mentioned this over at the other question, but it bears repeating. If you have a private well, read this.. There are links to the bottom for state certified testing agencies. If you've never had your water tested, I highly recommend doing so immediately, beer brewing notwithstanding - it's potentially a serious safety issue.
If you are on city water, then it's probably safe, but I'd be tempted to test what's coming out of your individual tap just to be sure.
The best place I've found for water testing is www.wardlab.com. Get test W-6. It runs about $16 and gives you all the info you need for brewing. If you tell them you're a homebrewer, they have special info available.