We present deep images of nine nearby edge-on galaxies in the Ho: line, with the goal of understanding the frequency of occurrence and physical properties of extraplanar (above the H Il region layer) diffuse ionized gas (DIG). None of the nine galaxies shows an extraplanar layer as bright or as widespread as those of NGC 891 or NGC 5775. Most galaxies show only a few patches or a few filaments of extraplanar gas. Others show no detectable extraplanar gas at all. Modeling of the most edge-on galaxies shows that vertical columns of emission measure for these patches (2-9 pc cm(-6)) are comparable to those of the local Reynolds layer, although there are uncertainties such as the extent of the emission region along the line of sight. It is therefore probably the case that the typical spiral galaxy has extraplanar DIG in only a few isolated regions, presumably above sites of active star formation, and perhaps concentrated to spiral arms. Considering these and previously observed galaxies, a clear correlation has emerged that the galaxies with the highest star formation rates or star formation rates per unit area generally have the most widespread and brightest extraplanar H alpha emission. This is in agreement with the known relationship between extraplanar H alpha brightness and disk star formation along the major axis of NGC 891. The most prominent layer of extraplanar DIG is in NGC 4302, where emission is detectable out to a galactocentric radius of 4 kpc and a height of 2 kpc. The best studied galaxy in the sample, NGC 5907, shows no evidence for extraplanar DIG. However, it is inclined such that two-dimensional structure can be seen in the H II region distribution, which makes extraplanar gas difficult to detect. Nevertheless, a widespread layer like that of NGC 891 is unlikely to be present, but one associated with spiral arms and covering only a small fraction of the disk (as seems to be the case for M31) cannot be ruled out. Another interesting discovery is of a filamentary system above and below the center of NGC 4013. The filaments form an H shape centered on the nucleus and resemble a much larger system of filaments in NGC 3079. They are presumably gas swept up by a wind from a nuclear starburst. Two other galaxies also show loops or filaments above the nucleus, which suggests that, if they trace nuclear starbursts, such events are occurring in a nonnegligible fraction of normal spirals.