Time-Correlated Single Photon Counting (TCSPC) and time tagging of individual photon detections are powerful tools in many quantum optical experiments and other areas of applied physics. Using TCSPC, e.g., for the purpose of fluorescence lifetime measurements, is often limited in speed due to dead-time losses and pileup. We show that this limitation can be lifted by reducing the dead-time of the timing electronics to the absolute minimum imposed by the speed of the detector signals while maintaining high temporal resolution. A complementing approach to speedy data acquisition is parallelization by means of simultaneous readout of many detector channels. This puts high demands on the data throughput of the TCSPC system, especially in time tagging of individual photon arrivals. Here, we present a new design approach, supporting up to 16 input channels, an extremely short dead-time of 650 ps, very high time tagging throughput, and a timing resolution of 80 ps. In order to facilitate remote synchronization of multiple such instruments with highest precision, the new TCSPC electronics provide an interface for White Rabbit fiber optic networks. Beside fundamental research in the field of astronomy, such remote synchronization tasks arise routinely in quantum communication networks with node to node distances on the order of tens of kilometers. In addition to showing design features and benchmark results of new TCSPC electronics, we present application results from spectrally resolved and high-speed fluorescence lifetime imaging in medical research. We furthermore show how pulse-pileup occurring in the detector signals at high photon flux can be corrected for and how this data acquisition scheme performs in terms of accuracy and efficiency.