The focus of this paper is on improving the quality of streaming video transmitted over the Internet. The approach we investigate assumes the availability of multiple paths between the source and the destination, and dynamically selects the best one. Although this is not a new concept, our contribution is in estimating the "goodness" of a path from the perspective of the video stream, instead of relying only on raw network performance measures. The paper starts by showing that the use of raw network performance data to control path switching decisions can often result in poor choices from an application perspective, and then proceeds to develop a practical approach for evaluating, in real-time, the performance of different paths in terms of video quality. Those estimates are used to continuously select the path that yields the best possible transmission conditions for video streaming applications. We demonstrate the feasibility and performance of the scheme through experiments involving different types of videos.