Well, as water professional I can say for sure there many many cities in the US that have water you should not drink. This has nothing to do with taste as most things that actually pose a threat you cannot taste or smell.
In addition, two terms are typically used to state the accepted levels of contaminants in water: MCL (Maximum Contaminant Level) and MCLG (Maximum Contaminant Level Goal). These terms differ greatly. The MCL is what the cities and counties across the US are allowed to get away with. This means that things like cost, practicality, financial feasibility etc are considered when it's time to spend money on water purification leaving your health a little ways down the list, especially when sometimes big business lobbying becomes a part of the game.
The MCLG is the level of contaminant at which some peoples health will be affected. This is the number you watch if you are concerned about your health but NOT the number that cities and counties have to adhere to.
Therefore, if you care enough, you need to find out what's in your city's water, or you'll not know your own situation. Or save the hassle and buy an inexpensive Reverse Osmosis purifier.

A couple of myths:

1. I boil my water so I'm safe.
Many many contaminants do not evaporate like water, especially the really bad ones. So all you are doing is increasing the percentage of contaminants in relation to the amount of pure water which is evaporating.

2. Britta filters work great.
Britta and similar faucet and fridge filters are 99% carbon based. This means they will remove most things that smell or taste bad. But, with the exception of some chemicals they do little or nothing to remove many contaminants that are bad for you.

By the way, I'm not a health freak and I got my share of bad eating habits, just figured I'd share the facts.