Electric engines have a number of properties that are great for aviation, namely the ability to provide torque at low speeds and easily handle high rotation rates, which removes the need for complicated gearboxes and simplifies design. They have been proposed a number of times over the years, the historical problem has always been getting the electricity to drive things: batteries are heavy and diesel->electric converters (eg. hybrid trains) are too large to be practical.
It's worth pointing out that piston aircraft engines usually don't use gearboxes. Instead, they drive the propeller directly, which dictates very low engine speeds relative to where car engines usually produce their peak power since any part of the propeller blade nearing the speed of sound results in a loss of efficiency.
I wonder if progress being made in micro-turbine generators would one day allow them to be used in planes. Having a bank of generators inside the fuselage could making flying a lot safer. I imagine planes can be made much more aerodynamic as well.
Turbines are more efficient with larger sizes due to the fluid mechanics, and they need air, so then you end up at gas turbine engines externally mounted.
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