Quantization of energy is a quintessential characteristic of quantum systems. Here we analyze its effects on the operation of Otto cycle heat machines and show that energy quantization alone may alter and increase machine performance in terms of output power, efficiency, and even operation mode. Our results demonstrate that quantum thermodynamics enable the realization of classically inconceivable Otto machines, such as those with an incompressible working fluid. We propose to measure these effects experimentally using a laser-cooled trapped ion as a microscopic heat machine.