An extensive experimental study of the kinetics of capillary rise in borosilicate glass tubes of different sizes and cross-sectional shapes using various fluid systems and tube tilt angles is presented. The investigation is focused on the direct measurement of dynamic contact angle and its variation with the velocity of the moving meniscus (or capillary number) in capillary rise experiments. We investigated this relationship for different invading fluid densities, viscosities, and surface tensions. For circular tubes, the measured dynamic contact angles were used to obtain rise-versus-time values that agree more closely with their experimental counterparts (also reported in this study) than those predicted by Washburn equation using a fixed value of contact angle. We study the predictive capabilities of four empirical correlations available in the literature for velocity-dependence of dynamic contact angle by comparing their predicted trends against our measured values. We also present measurements of rise in noncircular capillary tubes where rapid advancement of arc menisci in the corners ahead of main terminal meniscus impacts the dynamics of rise. Using the extensive set of experimental data generated in this study, a new general empirical trend is presented for variation of normalized rise with dynamic contact angle that can be used in, for instance, dynamic pore-scale models of flow in porous media to predict multiphase flow behavior.