We report the results of an [O III] 5007 survey for planetary nebulae (PN) in three spiral galaxies: M101 (NGC 5457), M51 (NGC 5194/5195) and M96 (NGC 3368). By comparing on-band/off-band [O III] 5007 images with images taken in H-alpha and broadband R, we identify 65, 64 and 74 PN candidates in each galaxy, respectively. From these data, an adopted M31 distance of 770 kpc, and the empirical planetary nebula luminosity function (PNLF), we derive distances to M101, M51, and M96 of 7.7 +/- 0.5, 8.4 +/- 0.6, and 9.6 +/- 0.6 Mpc. These observations demonstrate that the PNLF technique can be successfully applied to late-type galaxies, and provide an important overlap between the Population I and Population II distance scales. Our observations also suggest that the cutoff in the [O III] luminosity function is insensitive in age. We discuss some special problems associated with using the PNLF in spiral galaxies, including the effects of dust and the possible presence of [O III] bright supernova remnants.