A standard homeowners insurance policy does not cover earthquake or flood damage. See list of perils covered by homeowners insurance.
Note that insurance policies generally distinguish between water damage arising from leaking pipes or sprinkler systems in your home (which you may be covered for) and flooding caused by groundwater and weather events. You should check your policy to determine your particular coverage.
Earthquake insurance can be purchased separately from most insurance companies and is generally issued as an endorsement to your homeowners insurance policy.
Flood insurance can also be purchased separately from some insurance companies. Depending on the location of your home, you may qualify for federal flood insurance. For more information about flood insurance, visit the National Flood Insurance Program.