We present total and polarized intensity images of 15 active galactic nuclei obtained with the Very Long Baseline Array at 7 mm wavelength at 17 epochs from 1998 March to 2001 April. At some epochs the images are accompanied by nearly simultaneous polarization measurements at 3 mm, 1.35/0.85 mm, and optical wavelengths. Here we analyze the 7 mm images to define the properties of the jets of two radio galaxies, five BL Lac objects, and eight quasars on angular scales ≳0.1 mas. We determine the apparent velocities of 106 features in the jets. For many of the features we derive Doppler factors using a new method based on a comparison of the timescale of decline in flux density with the light-travel time across the emitting region. This allows us to estimate the Lorentz factors (Γ), intrinsic brightness temperatures, and viewing angles of 73 superluminal knots, as well as the opening angle of the jet for each source. The Lorentz factors of the jet flows in the different blazars range from Γ ∼ 5 to 40 with the majority of the quasar components having Γ ∼ 16-18, while the values in the BL Lac objects are more uniformly distributed. The brightest knots in the quasars have the highest apparent speeds, while the more slowly moving components are pronounced in the BL Lac objects. The quasars in our sample have similar opening angles and marginally smaller viewing angles than the BL Lacs. The two radio galaxies have lower Lorentz factors and wider viewing angles than the blazars. Opening angle and Lorentz factor are inversely proportional, as predicted by gasdynamical models. The brightness temperature drops more abruptly with distance from the core in the BL Lac objects than in the quasars and radio galaxies, perhaps owing to stronger magnetic fields in the former resulting in more severe synchrotron losses of the highest energy electrons. In nine sources we detect statistically meaningful deviations from ballistic motion, with the majority of components accelerating with distance from the core. In six sources we identify jet features with characteristics of trailing shocks that form behind the primary strong perturbations in jet simulations. The apparent speeds of these components increase with distance from the core, suggestive of acceleration of the underlying jet.