When more than one appliance is served by a single circuit, there is a potential for these appliances to draw more power than the circuit is designed to handle. The result of a circuit overload is a tripped circuit breaker or fuse.
The National Electrical Code requires that any appliance or device dedicated as critical-use be served by its own dedicated circuit to eliminate the chance of another appliance or device tripping the breaker and shutting down that critical fixture. These critical appliances include things like furnaces, water heaters, sump pumps, even refrigerators. If one of these breakers trips and you don't know it, you could end up with a flooded basement, a freezing house, no hot water, or a refrigerator full of rotten food.