Bonus: Koopas, Paratroopas, Buzzy Beetles can be knocked back into their shells, but they DO come out again, so they're not "killed."
Bowser, Spinys, Spiny Eggs, Piranha Plants, Bloopers, Koopas and Paratroopas can't be (completely) defeated via stomping, but CAN with a Fireball.
Podoboo, Firebar, and Buzzy Beetle can't be defeated, although Buzzy Beetles can be when careened with a shell.
Actual stompable (AND defeated) enemies: Goomba, Hammer Bros. and Cheep Cheep (out of water)
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Deep inside us all is a little green elf telling us to burn things.