We have mapped 16 edge-on galaxies at 20 cm using the Very Large Array in its C configuration, and a subset of these galaxies in the D configuration at 6 and/or 20 cm, in a search for extended (1 kpc) radio continuum emission above and below the plane. For five galaxies, we could form spectral index, energy, and magnetic field maps (assuming minimum energy). While the galaxies were partly chosen by radio flux density, they span a variety of star formation rates (SFRs), and only six might be considered starburst galaxies. A range of Hubble type and degree of isolation are also represented. The galaxies largely fall on the FIR–radio continuum correlation. They also display a correlation between IR surface brightness and warmth, extending the previously observed relation of Lehnert & Heckman to galaxies with lower star formation rates. We find that all but one galaxy show evidence for nonthermal high-latitude radio continuum emission, suggesting that cosmic-ray (CR) halos are common in star-forming galaxies. Of these, eight galaxies are new detections. The high-latitude emission is seen over a variety of spatial scales and in discrete and/or smooth features. In some cases, discrete features are seen on large scales, suggesting that smooth radio halos may consist, in part, of discrete features combined with low spatial resolution. In general, the discrete features emanate from the disk, but estimates of CR diffusion lengths suggest that diffusion alone is insufficient to transport the particles to the high latitudes seen (>15 kpc in one case). Thus CRs likely diffuse through low-density regions and/or are assisted by other mechanisms (e.g., winds). We searched for correlations between the prevalence of high-latitude radio emission and a number of other properties, including the global SFR, supernova input rate per unit star-forming area, A, and environment, and do not find clear correlations with any of these properties. A subset of the data allows, at best, for only a weak correlation with A. Our one nondetection (NGC 4517), however, occurs at a threshold level consistent with that found by Dahlem, Lisenfeld, & Golla. The lack of a good correlation with star formation indicators could be the result of the different timescales for star formation processes compared with the duration of the radio emission. Correlations with other properties, such as environment, are more difficult to assess. However, a few isolated galaxies display strong radio halos, indicating that an interaction is not necessary to produce the extraplanar emission.