Outdoor pumps should always use a grounded, 3-wire plug. Indoor fountains sometimes have 2-wire and sometimes 3-wire plugs. For people wanting a really thin cord, 2-wire pumps provide the more aesthetic experience. Some retail stores require 3-wire pumps even for indoor fountains (though, ironically, they might not for aquarium pumps), and these thicker cords can be hidden by plants, stones, or other decorations. All pumps must be connected to a GFI outlet for safety.
95% of the time the customer has let the pumps get hot by running them dry. Most fountain pumps are water-cooled and once the fountain is dry they burn up. Usually there is nothing you can do about this other than to buy a new pump. Also, however, pumps are supposed to be cleaned every so often by opening up the impeller case on the fountain pump. Follow the manufacturer’s directions.