With the tremendous advancement of deep learning and communication technology, Vehicle-to-Everything (V2X) cooperative perception has the potential to address limitations in sensing distant objects and occlusion for a single-agent perception system. V2X cooperative perception systems are software systems characterized by diverse sensor types and cooperative agents, varying fusion schemes, and operation under different communication conditions. Therefore, their complex composition gives rise to numerous operational challenges. Furthermore, when cooperative perception systems produce erroneous predictions, the types of errors and their underlying causes remain insufficiently explored. To bridge this gap, we take an initial step by conducting an empirical study of V2X cooperative perception. To systematically evaluate the impact of cooperative perception on the ego vehicle's perception performance, we identify and analyze six prevalent error patterns in cooperative perception systems. We further conduct a systematic evaluation of the critical components of these systems through our large-scale study and identify the following key findings: (1) The LiDAR-based cooperation configuration exhibits the highest perception performance; (2) Vehicle-to-infrastructure (V2I) and vehicle-to-vehicle (V2V) communication exhibit distinct cooperative perception performance under different fusion schemes; (3) Increased cooperative perception errors may result in a higher frequency of driving violations; (4) Cooperative perception systems are not robust against communication interference when running online. Our results reveal potential risks and vulnerabilities in critical components of cooperative perception systems. We hope that our findings can better promote the design and repair of cooperative perception systems.