Another potential problem concerns variability in the chemical properties of your water supply over time (e.g., month-to-month). Some water districts don't have enough water themselves, forcing them to purchase additional water from neighboring water districts in times of shortages. If this water has a different chemical properties (e.g., hardness), your tap water's chemistry will vary as well. As a common example, high bacteria levels are more of a problem in summer than winter, especially in warmer climates. Consequently, it is not uncommon for water companies to use more chlorine in summer months to keep bacteria in check. Even such factors as local weather can have an impact; heavy rains may cause the hardness of your water supply to decrease as local reservoirs fill.
In general, chlorine and chloramine are the two additives that cause the most problems. Note that these two substances are VERY DIFFERENT! Be sure you know what is in your tap water and treat appropriately.
Chlorine at high concentrations is toxic to fish; at lower concentrations, it stresses fish by damaging their gills. Concentrations of as little as 0.2-0.3 ppm kill most fish fairly rapidly. To prevent stress, concentrations as low as 0.003 ppm may be required. Fortunately, chlorine can easily be removed from water by the chemical sodium thiosulfate, readily available at fish stores under various brands. Sodium thiosulfate neutralizes chlorine instantly. Note that there are many ``water treatment'' products that are advertised as ``making tap water safe''. Read labels carefully. Inevitably, the ones that neutralize chlorine all contain sodium thiosulfate, plus other substances that may or may not be useful. If your water only contains chlorine (as opposed to chloramine), sodium thiosulfate is all you need. The most cost-effective treatments use only 1 drop per gallon of water. Most other water treatments are much more expensive in the long-term; they may require a teaspoon of treatment (or more) per gallon!
Chlorine is relatively unstable in water, escaping to the atmosphere on its own. Water left in a bucket (or tank) with adequate water circulation (e.g. filter or airstone) will be free of chlorine in 24 hours or less.
Many netters report that they perform partial water changes without ever treating their tap water to remove chlorine. Keep in mind that even though fish show no APPARENT ill effects from untreated water, that doesn't mean that the chlorine isn't stressing your fish. How much stress depends on how much chlorine is introduced to the tank, which depends on many factors (including the percentage of new water added). Because chlorine removers are so cheap (pennies per usage), the insurance they provide should not be passed up.
Chloramine poses two significant headaches for aquarists. First, chlorine-neutralizing chemicals such as sodium thiosulfate only neutralize the chlorine portion of the chloramine, neglecting an even bigger problem: deadly ammonia. The consequences can be devastating to fish. Although a tank's biological filter will (eventually) convert the ammonia to nitrate, the time it takes to do so may be longer than what your fish can tolerate.
The second problem relates to water changes. One of the primary reasons for doing regular water changes is to remove nitrates that build up. If your replacement tap water contains ammonia, you'll be putting nitrogen right back into your tank and it will be impossible to reduce the nitrates below the concentration in your tap water. Fortunately, tap water concentrations are relatively low (1 or 2 ppm); you are more likely to have a much higher concentration of nitrate in your tank.
Chloramine can be safely neutralized through such products as Amquel, which neutralize both the ammonia and chlorine portions of the chloramine molecules. The neutralized ammonia will still be converted to nitrates via a biological filter.
Another method for neutralizing chloramine is to age the water while simultaneously performing biological filtration. For example, get an appropriately-sized (plastic) garbage can, fill it with tap water, dechlorinate it with sodium thiosulfate, and then connect an established biological filter to it. Just as in your tank, the bio filter will convert the ammonia to nitrate, after which it can safely be added to your tank. Note: you must add sodium thiosulfate to neutralize the chlorine; otherwise, the chloramine will kill the bacteria in your biological filter.
Alternatively, the ammonia can removed by filtering the water through zeolite or carbon before adding it to your tank. [Note: folks report mixed success with this. If you have concrete (positive or negative) experience to report, please notify the FAQ maintainers.]
One potential problem with using well water is that it frequently contains high concentrations of dissolved gases (which may be dangerous to fish). For example, well water is frequently supersaturated with CO2, which lowers the water's pH. Once the CO2 escapes, the pH will increase. Fish shouldn't be subjected to this temporary pH fluctuation. For safety, aerate well water thoroughly for several hours before adding it to your tank.