A freezer is possibly another such use case, if it keeps the temperature to within +/- X degrees of the set temperature, it can delay kicking in during periods of expensive electricity, and over-cool during periods of cheap electricity.
I could load the washer or dryer and program it to run it when it's cheapest if I'm not in a hurry.
Charging an electric car could work the same way.
Air conditioners are a huge deal, my single biggest electricity consumer. In a world where things were smarter they would chill coolant/water/ice during times of cheap electricity, and that would be used to cool during the hot evenings.
The problem is I have no way to take advantage of any of that. The electric grid isn't giving me feedback on the spot price of electricity (and in many places they don't even break it down on the bill, showing just one value for $/kwH for the entire month - that's what my bill looks like.)
Even if that problem is resolved, my appliances are too dumb to take advantage of that information to optimize my costs.
The grid needs to convey the realtime pricing information to customers, and then smarter appliances will be developed to take advantage of that information. The market may be able to do a surprisingly effective job of moderating demand itself if both the information and the means to apply it are available.