We demonstrate highly efficient cavity ringdown spectroscopy in which a broad-bandwidth optical frequency comb is coherently coupled to a high-finesse optical cavity that acts as the sample chamber. 125,000 optical comb components, each coupled into a specific longitudinal cavity mode, undergo ringdown decays when the cavity input is shut off. Sensitive intracavity absorption information is simultaneously available across 100 nanometers in the visible and near-infrared spectral regions. Real-time, quantitative measurements were made of the trace presence, the transition strengths and linewidths, and the population redistributions due to collisions and the temperature changes for molecules such as C2H2, O2, H2O, and NH3.