A search of 17 globular clusters for radio emission at a wavelength of 20 cm was conducted. Resolutions comparable to the cluster core diameters were employed to maximize sensitivity to integrated emission from a possible population of pulsars in a cluster. New sources were detected in the clusters Terzan 5, NGC 6440, NGC 6539, and NGC 6544, and the existence of a controversial radio source in NGC 6624 was confirmed. Measurements of variability and spectral dependence, and subsequent pulsed searches, suggest that, with the possible exception of the source in NGC 6624, all of the detected flux density is due to pulsars. Assuming the standard pulsar luminosity function, it is concluded that Terzan 5 and NGC 6640 each contain about 50 pulsars which beam toward earth, that the total number of such objects in the Galactic globular system most likely lies between 500 and 2000, and that the expected number of pulsars in a globular cluster depends only weakly on the stellar collision rate.