We propose a general quality-power adaptation framework that controls the perceived video quality and the length of viewing time on battery-powered video receivers. The framework can be used for standalone video devices (e.g., DVD players and notebooks) as well as mobile receivers obtaining video signals from wireless networks (e.g., mobile TV and video streaming over WiMAX). Furthermore, the framework supports both live streams (e.g., live TV shows) and pre-encoded video streams (e.g., DVD movies). We present an adaptation algorithm for each mobile device to determine the optimal substream that can be received, decoded, and rendered to the user at the: (i) highest quality for a given viewing time, and (ii) longest viewing time for a given quality without exceeding the battery level constraint. We instantiate this framework and work out its details for mobile video broadcast networks. In particular, we propose a new video broadcast scheme that enables mobile video devices to efficiently adapt scalable video streams and achieve power saving proportional to the bit rates of the received streams. We implement the proposed framework in an actual mobile video streaming testbed and we conduct experiments using real video streams broadcast to mobile phones. These experiments show the practicality of the proposed framework and the possibility of achieving viewing time scalability. For example, on a mobile phone receiving and decoding the same video program, a viewing time in the range from 4 to 11 hours can be achieved by adaptively controlling the frame rate and visual quality of the video stream.