Several factors will influence when and how often you test your water. Where do get your water from? Has that source changed? Have you done any plumbing changes lately? Is there reason to believe that your water is contaminated? Is there a sickness or illness in your family affecting more than one person and over a longer than normal time period?
If you receive your water from a "Public Supply", i.e., a municipal supply, or a supply that provides water to more than 25 persons for 60 days per year (some states are different -- check with YOUR local water department), you can be fairly certain that the water supply is checked on a regular basis. The frequency of the testing is based on the number of people served, and may vary from more than once per week to once per month, or even less. Under these conditions, test when you move into a new residence to acquire a "base line" of contaminant level, if any. Retest every three years, unless you have reason to believe that something has changed that could affect the quality of your water.
If you have a private well, you are the only person who is responsible for the water your family drinks and bathes in. I recommend testing by your local Health Department every six months for Bacteria and Nitrate. These two tests serve as indicators for other types of contamination -- that is not to say forget the other tests; just that if you get a "bad" test from them, you should also retest for the other types of contaminants as well. Private wells should be tested on a regular basis for Pesticides, Herbicides, Metals, Organic and Inorganic chemicals and volatiles. Currently, no laws govern the frequency of such testing -- that is why I say YOU are the only person responsible for your family's water. I recommend an initial test (for a base line), and then at least once per year. Remember, one day after testing and finding "no contaminants", your source could become contaminated.