The short answer is usually. But no one puts stock in the short answer.
Ask any coffee enthusiast if the type of water matters in their coffee and everyone of them will (read: should) say yes. The three types of water available to the average household are usually filtered, tap and bottled water. To quickly rule out one option, I would agree with the growing number of people that bottled water is indeed a waste of money and resources, especially since numerous bottled waters are practically the same as tap water in terms of health and taste benefits.
That leaves the duel between tap and filtered water, with the two issues being health effects and taste. Depending on where you are, your tap water can contain harmful agents that you might not want in your body. But at the same time, there are some regions of the country with exceptional tap water. So, it really comes down to your specific geographical source and hygenic philosophy as to whether filtering offers any real benefits for your health.
And then there was taste. Since coffee is mostly water, clearly the water you use to brew your coffee will make a severe impact on the taste of your coffee. Thus, while I know some cities boast amazing tap water, we're all not so lucky. Thus, I took up an offer from Pur to test out a Pur Water Pitcher to see if it made a difference in the taste of my coffee versus coffee brewed with my tap water.
While I do not have the specific information on the health qualities of my local water system, I would say that it ranks fairly high in taste comparatively to other taps I've tapped. As for my methods of testing, I compared my tap water versus the filtered water in both glasses of water and in cups of coffee.
Drinking the water straight up, my tap water produced an alkali-esque quality in the aftertaste compared to the Pur water which had a much brighter and sweeter flavor to it. This held true through multiple trials and even when my wife produced me a blind taste test, I was able to differentiate the tap and the filtered.
As for my coffee, the results were similar. The coffee brewed via the filtered water was a little sweeter and acidic in taste while the tap water produced coffee slightly more basic with a metallic aftertaste.
Thus, I can vouch that the Pur Water Pitcher did make a noticeable difference in the taste of my water and coffee. If you're looking to get better tasting water from your tap, a water filter could do it for you though there's no guarantees. And if you like being uber careful about possible threats in your water, then filtration will definitely help you sleep better (whether it really does the job, only time will tell).
So if you have less-then-stellar tap water and/or you want to take a step in the direction of water safety, then try out a Pur Water Pitcher.
note: pitcher was provided free of charge and the above review is objective feedback.