We present the results of an analysis of relativistic jet apparent speeds from VLBI images in the Radio Reference Frame Image Database (RRFID). The images are snapshot VLBI images at 8 and 2 GHz using the VLBA, plus up to 10 additional antennas that provide global VLBI coverage. We have analyzed the 8 GHz images from the first 5 years of the database (1994-1998), for all sources observed at three or more epochs during this time range. This subset comprises 966 images of 87 sources. The sources in this subset have an average of 11 epochs of observation over the years 1994-1998, with the best-observed sources having 19 epochs. About half of the sources in this RRFID kinematic survey have not been previously studied with multiepoch VLBI observations. We have measured apparent speeds for a total of 184 jet components in 77 sources, of which the best-measured 94 component speeds in 54 sources are used in the final analysis. The apparent speed distribution shows a peak at low apparent speeds (consistent with stationary components), a tail extending out to apparent speeds of about 30c, and a mean apparent speed of 3.6c. A total of 36 of the sources in this paper are also included in the 2 cm VLBA survey by Kellermann et al., with similar angular resolution, sensitivity, and time range. For those sources, we present a detailed component-by-component comparison of the apparent speeds measured by the 2 cm survey and those measured in this paper. Many of the independent apparent speed measurements agree very well, but for approximately 25% of the components we find significant differences in the apparent speeds measured by the two surveys. The leading cause of these discrepancies is differences in how the two surveys have identified jet components from epoch to epoch.