VRI photometric observations of surface-brightness fluctuation in 13 Virgo Cluster galaxies, M32, and NGC 3379, obtained using an 800 x 800 CCD array on the 4-m telescope at KPNO during March 1989, are reported. The data-reduction techniques are described in detail, and the results are presented in tables and graphs. Particular attention is given to distance estimates derived from the I-band fluctuations: it is shown that NGC 4365 is behind the cluster, while NGC 4468 and NGC 4489 are in the foreground. The average distance to the cluster is found to be 17 + or - 1 Mpc, with H0 = 78 + or - 6 km/sec Mpc; the corresponding values from a direct isochrone calibration are 21 Mpc and 64 + or - 5 km/sec Mpc.