Commonly, saccades are thought to be ballistic eye movements, not modified during flight, with a straight path and a well-described velocity profile. However, they do not always follow a straight path and studies of saccade curvature have been reported previously. In a prior study, we developed a real-time, saccade-trajectory prediction algorithm to improve the updating of gaze-contingent displays and found that saccades with a curved path or that deviated from the expected velocity profile were not well fit by our saccade-prediction algorithm (velocity-profile deviation), and thus had larger updating errors than saccades that had a straight path and had a velocity profile that was fit well by the model. Further, we noticed that the curved saccades and saccades with high velocity-profile deviations were more common than we had expected when participants performed a natural-viewing task. Since those saccades caused larger display updating errors, we sought a better understanding of them. Here we examine factors that could affect curvature and velocity profile of saccades using a pool of 218,744 saccades from 71 participants watching "Hollywood" video clips. Those factors included characteristics of the participants (e.g., age), of the videos (importance of faces for following the story, genre), of the saccade (e.g., magnitude, direction), time during the session (e.g., fatigue) and presence and timing of scene cuts. While viewing the video clips, saccades were most likely horizontal or vertical over oblique. Measured curvature and velocity-profile deviation had continuous, skewed frequency distributions. We used mixed-effects regression models that included cubic terms and found a complex relationship between curvature, velocity-profile deviation and saccade duration (or magnitude). Curvature and velocity-profile deviation were related to some video-dependent features such as lighting, face presence, or nature and human figure content. Time during the session was a predictor for velocity profile deviations. Further, we found a relationship for saccades that were in flight at the time of a scene cut to have higher velocity-profile deviations and lower curvature in univariable models. Saccades characteristics vary with a variety of factors, which suggests complex interactions between oculomotor control and scene content that could be explored further.