It depends on the vehicle. Power steering can either be electric (EPS) or mechanical, with a compressor that's belt-driven off the engine. My Civic has rack-and

It depends on the vehicle. Power steering can either be electric (EPS) or mechanical, with a compressor that's belt-driven off the engine. My Civic has rack-and-pinion steering with EPS. When the engine is off, it's still steerable, but there's no power assist. But you don't want to turn the ignition lock all the way off, because that does lock the steering wheel.