Why is Hydrazine used to power the F-16's EPU?
To fill the voids in aeroalias' answer:

Hydrazine is a monopropellant, something which does not need to be mixed and burned to free up the energy contained in its chemical bonds. This energy is freed by letting the hydrazine stream over a catalyst, in case of the F-16 EPU that is iridium. This breaks the chemical bond, producing ammonia, nitrogen gas, hydrogen gas and heat which converts the water into steam. Heating increases the volume of the gasses and the steam so they pick up speed, just like the gasses in the combustion chamber of a jet engine. In the catalyst chamber of the F-16's EPU the temperature reaches more than 800°C in just a couple of milliseconds, and no combustion is involved! This high-pressure, high-speed gas flows through a small turbine which in turn drives a generator and supplies hydraulic pressure.

Compression is not needed because pressure is supplied from the bottle containing the hydrazine-water mixture. Using a monopropellant also avoids any ignition problems and makes the setup very simple. Since hydrazine is quite stable at high pressure and ambient temperature, the shelf life of a hydrazine engine is high, and the liquid state of the hydrazine-water mixture makes its storage very compact. Just what you need in a fighter aircraft.