In general, most of the chemicals or microbes that can affect human health cannot be seen, tasted, or smelled in drinking water. Most health-related contaminants can only be identified through water testing.
However, you may suspect that your water is unsafe if you notice sudden changes in taste or odor. Consider testing for bacteria if you notice a sudden change in your water quality.
If there is a distinctive odor in your water, such as a smell of gasoline or a "chemical" smell, it is possible that your water is contaminated. However, many of the objectionable taste, color and odor problems are often not a concern for health. For example, that "rotten egg" smell may be naturally occurring hydrogen sulfide. A brownish-orange stain often indicates naturally occurring iron in groundwater.
For information and recommendations on testing your private well water, please refer to Testing Recommendations for Private Drinking Water Wells.