It would depend on what happened to the water heater and what type of policy you have. If the water heater is damaged in a fire, or a tornado, you should have coverage. A "special form" insurance policy will normally cover damage from a burst water heater, so they will pay for the clean up of the water but not to replace the water heater it's self, since it was the cause of the claim.
Remember, an insurance policy is for damage, but not maintenance. So if it quits, or doesn't function like it is supposed to, that is an expense you would have to absorb. If the water heater is damaged by a "Covered peril" (refer to your contract) - then yes, it is part of the house and covered like anything else.
Founder, City Building Owners Insurance, Somers, NY
As Dan mentioned, the answer depends on what caused the water heater to malfunction. If the water heater reached the end of its life, then the resulting water damage might be covered, depending on the specifics of your insurance policy, but you would likely be responsible for replacing the water heater, as well as for any related plumbing bills.
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Remember, an insurance policy is for damage, but not maintenance. So if it quits, or doesn't function like it is supposed to, that is an expense you would have to absorb. If the water heater is damaged by a "Covered peril" (refer to your contract) - then yes, it is part of the house and covered like anything else.