Most on-demand instant water heaters are not marine rated, and many are forbidden by insurance regulations, so you need to check with your insurance company if you want to go that route.
As for regular, tank-based water heaters. The most common size is about 6 gallons. Usually the hot water heater has a hydronic heating coil so that it can be heated using the engine coolant. Most will also have a heating element for when the boat is connected to 110 VAC shore power.
One thing to really watch out for with the hydronic, engine coolant heat exchanger type units is the water temps are often far hotter than you'd find in a domestic water heater and you're likely to scald yourself if you're not extremely careful. I'd recommend adding a tempering valve to keep the water temps in a reasonable range and prevent the risk of scalding.
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You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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Still—DON'T READ THAT POST AGAIN.