This Android app turns off the display's backlight without turning off the screen, saving battery (root)

Well, this is Android, which means you don't have to! The app Screen Backlight OFF lets you switch off your LCD display's backlight without turning off the screen itself. Thus, the device will stay awake, media playback will continue, but the screen won't eat up battery. To turn the backlight on again, simply tap the screen. That's all there's to it! However, SBO is a root app, so don't bother with it if your device isn't rooted.

SBO controls with a button residing inside the notifications drawer, which means you can access it from anywhere. It also features a configurable activation delay time, if you need it. It can also let other apps - such as automation tools like Tasker - use it to switch off the backlight.

Screen Backlight Off is a paid app, but members of the XDA Developer board can sideload it for free.