Following the discovery in the 1960s of radio and optical QSOs it was found that some of them lie very close to low-redshift (z ≤ 0.01) spiral galaxies with separations of 2 arcmin. These were discovered both serendipitously by many observers, and systematically by Arp. They are some of the brightest QSOs in radio and optical wavelengths and are very rare. We have carried out a new statistical analysis of most of those galaxy-QSO pairs and find that the configurations have high statistical significance. We show that gravitational microlensing due to stars or other dark objects in the halos of the galaxies apparently cannot account for the excess. Sampling or identification bias likewise seems unable to explain it. Following this up we selected all ~4000 QSOs with g ≤ 18 from a catalog of confirmed QSOs in the Sloan Digital Sky Survey, and compared them with various subsets of galaxies from the RC 3 galaxy catalog. In contrast to the earlier results, no significant excess of such QSOs was found around these galaxies. Possible reasons for the discrepancy are discussed.