Recently, in one of my transactions, we discovered arsenic in the well water. Arsenic is a toxin, meaning it is not very good for you, and in municipal water systems it is generally tested for. But if you buy a home with a well, you need to do the testing yourself as part of your inspection, and generally, this test is NOT included in a standard well water quality inspection. (Neither is radon). Both arsenic and radon are more expensive tests, but as they both present health concerns, should be tested for by every buyer of well water.
Some general facts are about arsenic:
1) It is both naturally occurring and man-made
2) The EPA limit for health is 10 ppb (parts per billion)
3) It can be treated - special systems can be used to remove the arsenic from the water.
4) It is probably best to treat it with a whole house system. That removes it from the shower, baths, and kitchen, all at the source.
and you can read more about it here: http://en.wikipedia.org/wiki/Arsenic
Cost of Water Treatment Systems for Arsenic
The systems aren't cheap - they can run from 2500-6000 - so it's advisable to do the test before purchasing, it certainly is not what you want to be doing as your first renovation.