We present a study on the end-to-end performance of a cooperative diversity system over random fading channels at high signal-to-noise ratio (SNR). The performance criteria we consider are the average symbol error probability (SEP) and outage probability. At high SNR, both average SEP and outage probability can be characterized by two parameters: the diversity and coding gains. We provide analytical results on the diversity and coding gains of a general cooperative system with multiple branches each with multiple hops. The results apply to arbitrary fading types (e.g., Rayleigh, Rician, or Nakagami), and the obtained simple expressions offer insight for understanding performance limiting factors in cooperative diversity systems.