Edit: others beat me to the punch on both the Peltier and piezoelectric effects.
For what it’s worth, the term “thermocouple” conventionally refers to a thermoelectric temperature sensor, while a non-sensor device for making significant electric power from a temperature differential is usually called a Peltier device. It’s not wrong to call a Peltier device a thermocouple, of course.
Whatever you call them, thermoelectric devices work both ways: they can use a temperature differential to produce electricity or they can use electricity to produce a temperature differential. (Plugging in a Peltier device makes one side cold and the other side hot).
In this way, they’re much like spinning magnets and copper coils. If you apply motion, you get electricity. If you apply electricity, you get motion.
Peltier devices are often used in both satellites (to generate power) and cheap dorm fridges (to chill cheap beer). They’re solid-state, so they’re much quieter than a compressor-based refrigerator, but they’re also a lot less efficient than a compressor-based fridge, which is why your kitchen fridge uses a compressor.
Fuel cells are used all the time, but only for niche applications—often for spacecraft. Honda has done a lot of research on the use of hydrogen fuel cells in cars. It works, but storing hydrogen slush in cars is nontrivial.
There are lots of ways to make electricity without spinning magnets in an electric field, but most of those methods are less efficient and/or more expensive than the alternative.
There has been a fair amount of research into harvesting energy using piezoelectric materials. These convert motion (usually bending) directly into high-voltage, low-current electricity. (They also convert electricity directly into motion). But for a given cost, you’ll usually make more electricity from the same motion with spinning magnets, so this is another niche technology.
