What legal action is available for water damage done to our home by neighbors pipe burst and flooding into our home?

Depending on the particular facts, you may have a claim against your neighbors for negligence resulting in the damage to your home, and/or for the manufacturer, seller of the sprinkler pipe, installer, repair people, etc. if any of their negligence caused the problem.  You will have a more difficult time with this latter group, since you had no direct dealings with them and therefore they may owe you no duty.  Any one or more of these defendants may have insurance which mightl cover this claim.