We report an extensive search for 22 GHz H2O maser emission from nearby active galaxies. Our sample includes all Seyfert and LINER galaxies listed in the Huchra catalog or the Veron-Cetty & Veron catalog with recessional velocities less than 7000 km s(-1), and all Seyfert galaxies and LINERs in Huchra's catalog with m(b) less than or equal to 14. In addition to these distance- and magnitude-limited samples, we have also observed a number of active galaxies, including radio galaxies, at higher redshift. In all, some 354 galaxies have been surveyed. Ten new H2O megamaser sources have been detected, resulting in 16 galaxies that are currently known to contain H2O masers with isotropic luminosities greater than 20 L.. Of the observed active galaxies with cz <7000 km s(-1), 5.4% have detectable H2O megamaser emission. This fraction increases to 11% for those sources with cz <2000 km s(-1). The newly discovered megamaser sources were monitored on subsequent observing runs. The strength of the maser features varies for these sources, as they do for Galactic masers. Three of the galaxies have sufficient data to test for velocity changes of narrow maser components comparable in magnitude to those of the well-studied systemic features in NGC 4258. The maser line in one of these galaxies-NGC 2639-is found to have a systematic redward velocity drift of 6.6+/-0.4 km s(-1) yr(-1). No systematic velocity drifts are found for the other two sources. We also report large apparent velocity changes in the unusual broad H2O emission feature in NGC 1052.