The New York Times recently published an article stating that "More than 20 percent of the nation’s water treatment systems have violated key provisions of the Safe Drinking Water Act over the last five years, …"
When you live in a city it seems reasonable to rely on water department officials to test and maintain the quality of your water. So it's disheartening to read that 1 out of 5 US treatment systems are out of compliance. It is especially disturbing because water contaminants contribute to illness. The Times says contaminants are "linked to millions of instances of illness within the United States each year."
I have my own well, so it's up to me to get it tested. You can test a municipal water supply too if you want to make sure your water company is doing its job. The process requires you to send off a quart of water to a testing lab. It costs from $100 to $250 depending on the suite of tests you require. If you are in a city, you might organize your neighbors to contribute. If you are concerned at all about water quality, it's worth the money.
Control Laboratories is one facility that tests water. You can find many others by searching on the Internet.