For the most part, water is supplied in Anthem by Arizona-American Water Company, though there are a few homes on well water outside the residential developments, A quick search on the internet indicates that Arizona-American is planning to sell the water operations to EPCOR USA in 2012. EPCOR serves Fountain Hills AZ and is another big private water company. There are a variety of "private" water companies (for profit companies) supplying water in AZ. For the most part they are like having city water, but cost per gallon can be higher then city water in say Phoenix.
Once you pick a Buyer's agent, they can help you get answers specific to a given property, or you can call the water company to ask questions.