We present 1625 new 15 GHz (2 cm) VLBA images of 295 jets associated with active galactic nuclei (AGNs) from the MOJAVE and 2 cm VLBA surveys, spanning observations between 1994 August 31 and 2013 August 20. For 274 AGNs with at least 5 VLBA epochs, we have analyzed the kinematics of 961 individual bright features in their parsec-scale jets. A total of 122 of these jets have not been previously analyzed by the MOJAVE program. In the case of 451 jet features that had at least 10 epochs, we also examined their kinematics for possible accelerations. At least half of the well-sampled features have non-radial and/or accelerating trajectories, indicating that non-ballistic motion is common in AGN jets. Since it is impossible to extrapolate any accelerations that occurred before our monitoring period, we could only determine reliable ejection dates for of those features that had significant proper motions. The distribution of maximum apparent jet speeds in all 295 AGNs measured by our program to date is peaked below , with very few jets with apparent speeds above . The fastest speed in our survey is , measured in the jet of the quasar PKS 0805-07, and is indicative of a maximum jet Lorentz factor of ∼50 in the parent population. An envelope in the maximum jet speed versus redshift distribution of our sample provides additional evidence of this upper limit to the speeds of radio-emitting regions in parsec-scale AGN jets. The Fermi-LAT-detected gamma-ray AGNs in our sample have, on average, higher jet speeds than non-LAT-detected AGNs, indicating a strong correlation between parsec-scale jet speed and the gamma-ray Doppler boosting factor. We have identified 11 moderate-redshift () AGNs with fast apparent speeds () that are strong candidates for future TeV gamma-ray detection. Of the five gamma-ray loud narrow-lined Seyfert I AGNs in our sample, three show highly superluminal jet motions, while the others have sub-luminal speeds. This indicates that some narrow-lined Seyfert I AGNs possess powerful jets with Lorentz factors in excess of 10, and viewing angles less than , consistent with those of typical BL Lac objects and flat-spectrum radio quasars.