Android: One of the neatest Moto X features is that it turns the display on as soon as you pick it up. Gravity Screen takes this concept a bit further by sensing more movements and automatically turning the display on or off. Plus, it's available for all phones.
The app can detect when you put your phone in your pocket, lay it face down, or even when you move it while reading. If it detects it's in a state where the screen doesn't need to be on, it turns it off. If it thinks you want to use it, the display comes right back on. You can customise the sensitivity of the various sensors.