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Video watching time is a crucial measure for studying user watching behavior in online Internet video-on-demand (VoD) systems. It is important for system planning, user engagement understanding, and system quality evaluation. However, due to the limited access of user data in large-scale streaming systems, a systematic measurement, analysis, and modeling of video watching time is still missing. In this paper, we measure PPLive, one of the most popular commercial Internet VoD systems in China, over a three week period. We collect accurate user watching data of more than 100 million streaming sessions of more than 100 thousand distinct videos. Based on the measurement data, we characterize the distribution of watching time of different types of videos and reveal a number of interesting characteristics regarding the relation between video watching time and various video-related features (including video type, duration, and popularity). We further build a suite of mathematical models for characterizing these relationships. Extensive performance evaluation shows the high accuracy of these models as compared with commonly used data-mining based models. Our measurement and modeling results bring forth important insights for simulation, design, deployment, and evaluation of Internet VoD systems.