The objective of this study is to assess the seismic behavior of reinforced concrete bridges with skew-angled seat-type abutments through a performance-based methodology. Special attention is given to the exploration of variations in the seismic behavior of such bridges with respect to the angle of skew. Post-earthquake reconnaissance studies have reported that larger values of skew angle adversely affect performance. The idiosyncratic, "multi-phasic," behavior of skew bridges--observed during initial simulations of the present study--led to the development of a novel assessment methodology. This methodology is applied to a comprehensive database of bridges, which comprise combinations of a variety of geometric properties including: (1) number of spans, (2) number of columns per bent, (3) column-bent height, (4) span arrangement, and (5) abutment skew angle. An extensive set of nonlinear response history analyses were conducted using distinct suites of ground motions representing records for rock and soil sites, and another set that contained pronounced velocity pulses. The findings indicate that demand parameters for skew-abutment bridges--e.g., deck rotation, abutment unseating, and column drift ratio--are generally higher than those for straight bridges. Through detailed investigations of the sensitivity of various response parameters to variations in bridge geometry and ground motion characteristics, we observed that bridges with larger abutment skew angles bear a higher probability of collapse due to excessive rotations. We also found that shear keys can play a major role in abating deck rotations and thus the probability of collapse. It was further observed that the resultant peak ground velocity (PGVres) is the most efficient ground motion intensity measure (IM) for assessing skewed bridges' seismic response.