We present a comprehensive theory of dead-time effects on Time-Correlated Single Photon Counting (TCSPC) as used for fluorescence lifetime measurements, and develop a correction algorithm to remove these artifacts. We apply this algorithm to fluorescence lifetime measurements as well as to Fluorescence Lifetime Imaging Microscopy (FLIM), where rapid data acquisition is necessarily connected with high count rates. There, dead-time effects cannot be neglected, and lead to distortions in the observed lifetime image. The algorithm is quite general and completely independent of the particular nature of the measured signal. It can also be applied to any other single-event counting measurement with detector and/or electronics dead-time.