Seyfert galaxies commonly host compact jets spanning 10-100 pc scales, but larger structures are resolved out in long-baseline aperture synthesis surveys. Previous, targeted studies showed that kiloparsec-scale radio structures ( KSRs) may be a common feature of Seyfert and LINER galaxies, and the origin of KSRs may be starbursts or active galactic nuclei (AGNs). We report a new Very Large Array survey of a complete sample of Seyfert and LINER galaxies. Out of all of the surveyed radio-quiet sources, we find that 44% (19 out of 43) show extended radio structures at least 1 kpc in total extent that do not match the morphology of the disk or its associated star-forming regions. The detection rate is a lower limit owing to the combined effects of projection and resolution. The infrared colors of the KSR host galaxies are unremarkable compared to other Seyfert galaxies, and the large-scale outflows orient randomly with respect to the host galaxy axes. The KSR Seyfert galaxies instead stand out by deviating significantly from the far-infrared-radio correlation for star-forming galaxies, with tendency toward radio excess, and they are more likely to have a relatively luminous, compact radio source in the nucleus; these results argue that KSRs are powered by the AGNs rather than starbursts. The high detection rate indicates that Seyfert galaxies generate radio outflows over a significant fraction of their lifetime, which is much longer than the dynamical timescale of an AGNpowered jet but is comparable instead to the buoyancy timescale. The likely explanation is that the KSRs originate from jet plasma that has been decelerated by interaction with the nuclear interstellar medium ( ISM ). Based on a simple ram pressure argument, the kinetic power of the jet on kiloparsec scales is about 3 orders of magnitude weaker than the power of the jet on 10-100 pc scales. This result is consistent with the interaction model, in which case virtually all of the jet power must be lost to the ISM within the inner kiloparsec.