Our countertop purifiers remove contaminants in a multitude of ways, including filtration, water softening, reverse osmosis, ultrafiltration, deionization, and powdered activated carbon treatment (Wikipedia). This means that no matter how old the pipes in your building are, how much chlorine they used at the treatment plant, or how much dust is in your faucet, by the time the water reaches your mouth, it's been transformed from questionable to unquestionably quenching. (Try saying that 10 times fast)
So when we purify water, what exactly are we taking out? Well, for one thing, most tap water still has small amounts of particulate matter (in other words, dirt and sand). These can be taken out with a simple filter. But removing the visible contaminants can still leave behind minerals like calcium and magnesium, metals like lead and copper, and dangerous parasites like Giardia and Crytosporidium. Although the minerals and sand may make your water taste funny, drinking water that is contaminated with any of those dangerous viruses and bacteria can make you extremely sick.
If you're at home in your kitchen, then your countertop filter will remove these waterborne microbes. But if you're ever caught cooking in another country, then you may want to invest in the SteriPEN, a hand-held pen that kills bacteria, viruses, and protozoa. The UV light emitted by the pen zaps and kills the bugs, so you can drink up without fear of a tummy ache (or worse).
The pen has an optional solar charging case too, so if you decide to use the pen on your next camping trip, you can bring it along without having to worry about it running out of juice. One downside is that it only works to kill bacteria, viruses, and other organisms: to rid your water of the dirt and debris you'll have to get the water bottle prefilter, which fits on most wide-mouth bottles (like Nalgene).
At a price tag of $99.95 for the pen, $79.95 for the solar case, and $12.95 for the prefilter, this set certainly doesn't come cheap. But from the viewpoint of an avid hiker and frequent jet-setter, I'd say it's a small price to pay for clean water and peace of mind.