There are a few rubber band powered RC models out there, belive it or not. Small indoor jobbies done by guys just because they can and it sounded like a good idea at the time. (some are reported to have rather decent flight times as well). But in general, it's not a practical power source for RC.

Electrics are quiet and slime-free. Most common are the smaller park flyer sizes. These have low power output and the planes don't always handle winds very well. However, if you spend enough money, you can do anything with an electric that you can do with glow(nitro) or gas. The big advantage to the small electrics is that they can be safely flown in a park or large backyard.

Glow (aka nitro) has the hightest power-to-weight ratio out there. Glow engines are actually fairly easy to get working right once you get past the initial learning curve. But they are loud, and make a mess on your airplane. The fuel is also expensive, at $15-25 per gallon, depending.

Gasoline is cheaper than glow, so gas engines make sense in the larger sizes where fuel consumption is rather high. Also, many (but not all) of the large gas engines can trace design influcence back to small gas powered devices like leaf blowers and weedwackers. So, for the size, they are cheaper than Glow. But they don't produce as much power for the same displacement as Glow, and you have to deal with a spark ignition system.