(In order from most power-consuming to least power-consuming) There are some technologies that aim to reduce power when large sections of the screen are black (you might have heard of 'localized dimming' or 'dynamic contrast'), but these features are largely found in TVs where movies might actually have large swaths of black on screen. If you need to make just a few black pixels, you can't just turn off the backlight in that area, so the backlight is always on and we just block light for those few pixels) (This might make you ask 'Why?', but remember that the backlight does not have as fine-grained control as the pixels themselves. When an LCD is black, it is doing full light output, and then also blocking all of that light to create the appearence of black. Most LCD devices use a backlight which is always on.
This depends on the display technology being used.
