minimal power. AFAIK it's the only artificial light source that is near 100% efficient (minus the losses of the high-voltage inverter). It requires 100-200 volts or so of AC, but draws almost no current (it acts as a capacitive rather than a resistive load).
Funny thing is that if you wanted to drive EL wire with audio frequencies (different frequencies give different brightness and color) and decided to use a regular stereo, you'd have to get a huge amp to get the voltages you need (because amps are designed to drive low resistance loads) but the wire would only use microwatts of power.
You can run it off line voltage, but the low frequency means you'll get a dull glow.