We present a study of the intrinsic absorption lines in the ultraviolet spectra of Seyfert 1 galaxies. The study is based on spectra from the Hubble Space Telescope and includes the Seyfert 1 galaxies observed with the Faint Object Spectrograph and Goddard High-Resolution Spectrograph at spectral resolutions of λ/Δλ ≈1000-20,000 with good signal-to-noise ratios. We find that the fraction of Seyfert 1 galaxies that show intrinsic absorption associated with their active nuclei is more than one-half (10 of 17), which is much higher than previous estimates (3%-10%) based on IUE data. There is a one-to-one correspondence between Seyfert galaxies that show intrinsic UV absorption and X-ray warm absorbers, indicating that these two phenomena are related. Although our sample is not complete, we conclude that intrinsic absorption represents an important component that needs to be integrated into our overall physical picture of active galaxies. The intrinsic UV absorption is generally characterized by high ionization: C IV and N V are seen in all 10 Seyfert galaxies with detected absorption (in addition to Lyα), whereas Si IV is present in only four of these Seyfert galaxies, and Mg II absorption is detected only in NGC 4151. The absorption lines are blueshifted (or in a few cases at rest) with respect to the narrow emission lines, indicating that the absorbing gas is undergoing net radial outflow. At high resolution, the absorption often splits into distinct kinematic components that show a wide range in widths (20-400 km s-1 FWHM), indicating macroscopic motions (e.g., radial velocity subcomponents or turbulence) within a component. The strong absorption components have cores that are much deeper than the continuum flux levels, indicating that the regions responsible for these components lie completely outside of the broad emission-line regions. Additional information on the covering factors and column densities can be derived from the absorption profiles in the high-resolution spectra. The covering factor of the absorbing gas in the line of sight, relative to the total underlying emission, is Clos ≥ 0.86, on average. The global covering factor, which is the fraction of emission intercepted by the absorber averaged over all lines of sight, is Cglobal ≥ 0.5. Thus, structures covering large solid angles as seen by the central continuum source (e.g., spherical shells, sheets, or cones with large opening angles) are required. The individual absorptioncomponents show a wide range in C IV column densities (0.1-14 × 1014 cm-2), and the ratio of N V to C IV column density varies significantly from one absorption component to the next, even in the same Seyfert galaxy. Thus, the intrinsic absorption in a Seyfert 1 galaxy is typically comprised of distinct kinematic components that are characterized by a range in physical conditions (e.g., ionization parameter and hydrogen column density). Finally, we show evidence for extreme variability in the intrinsic absorption lines of NGC 3783. In addition to our earlier report of the appearance of a C IV absorption doublet at -560 km s-1 (relative to the emission lines) over 11 months, we have detected the appearance of another C IV doublet at -1420 km s-1 over 15 months. On the other hand, the C IV absorption lines of NGC 3516 and NGC 4151 were very stable over periods of 6 months and 4 years, respectively. Monitoring observations of individual Seyfert galaxies at higher time resolution are needed to distinguish between different sources of variability (variable ionization, motion of gas across the line of sight) and to determine the densities and radial locations of the absorption components.