Oops, it's happened again, the Chicago land flooding that is. With the Tunnel and Reservoir Plan, or more commonly known as the Chicago Deep Tunnel, still under construction (full completion not anticipated until 2019), many home owners with basements and crawlspaces below the ground level received much more water than the sump pumps could handle. Those without the flood insurance in place, finished basements, or even just appliances installed in the basement or crawlspace areas suffered the most.
There are a few home appliances that, because of their large size, are usually installed directly on the floor surface. With the basements and crawlspaces that are subject to flooding, such installations become very risky, and it would probably make sense to either elevate those appliances on some kind of a platform or relocate them to the first floor to prevent the possibility of flooding.
Some or all of the electrical and gas components (depending on the design) in water heaters, furnaces, washers, dryers, dishwashers, ranges, etc. are located in the lower part of the appliance enclosure. Often, even just a few inches of water might compromise those parts, making the operation of the appliance hazardous.
Yes, you're right: this may not happen. Just like the cell phone you've dropped into the sink, and after a few days of drying, it started operating again. But you've lost warranty on it now - cell phone manufacturers will have proof because there is a little sensor inside the phone which changes color after being exposed to moisture.
Flooded home appliances are unlikely to have such sensor, but because their electrical and gas components have been designed to operate in a dry environment, submersing them under water might cause unexpected problems, eventually leading to electrical shock and / or gas explosion. It's just like with a flooded car, even if it runs for a while, its electrical wiring and other components will start corroding and deteriorating, eventually causing the car to stop running, possibly even start a fire. It might happen after a week, month or even a year.
When you see "have it replaced " in the listings below, it applies to the whole appliance, and not just the parts. In many cases it might actually be cheaper to install a new appliance than have all the compromised parts replaced.
Flooded gas water heater - if the water level reaches the burner or gas regulator / temperature control - have it replaced. Moisture might cause corrosion of those parts and create hazardous conditions, including gas explosion. Also, soaked insulation under the exterior jacket will cause water body to corrode (same for electric).
Flooded electric water heater - depending on the size, they might have one or two heating elements. All submersed electrical connections and components (wires, terminals, relays, thermostat, etc.) will eventually corrode and create hazardous conditions / possible fire - have it replaced.
Flooded Gas Furnace - it's bad for any design. Up-flow, down-flow, horizontal - a few inches of water will most likely cover some of the gas or / and electric (electronic) components - have it replaced. If you're not sure how high the water level was before it receded, turn off the power to the furnace and remove the lower service panel - there might be a distinctive water line on the side walls, cover, or any other internal parts.
Flooded Electric Furnace - any electrical parts submerged under water require replacement. With an electrical furnace, it might actually be cheaper to replace the electrical parts, unless the blower and its motor were also affected - have it checked by a HVAC contractor.
Flooded washer / dishwasher - both have electrical wiring, motors, and other components installed in the lower portion of its enclosure - if submerged, have it replaced
Flooded clothes dryer - gas or electric will have a motor at the base, some wiring, gas valve / pressure regulator - if submerged, have it replaced
Flooded gas range - gas supply, regulator, and bottom burner may be at the very bottom (depending on the design) - if submerged, have it replaced
Flooded electric range - there are usually electrical connections, terminals, and the bottom heating element within the few inches from the floor level - if submerged, have it replaced
Sometimes, your appliance might be salvageable, but have a professional determine it ... It's for your own safety!