We present the results of a study of the globular cluster systems of six massive spiral galaxies, originally cataloged as low surface brightness (LSB) but here shown to span a wide range of surface brightness values, including two intermediate to LSB galaxies. We used the Advanced Camera for Surveys on-board Hubble Space Telescope to obtain photometry in the F475W and F775W bands and select sources with photometric and morphological properties consistent with those of globular clusters. A total of 206 candidates were identified in our target galaxies. From a direct comparison with the Galactic globular cluster system we derive specific frequency values for each galaxy that are in the expected range for late-type galaxies. We show that the globular cluster candidates in all galaxies have properties consistent with globular cluster systems of previously studied galaxies in terms of luminosity, sizes and color. We establish the presence of globular clusters in the two intermediate to LSB galaxies in our sample and show that their properties do not have any significant deviation from the behavior observed in the other sample galaxies, implying that these properties do not evolve with the surface brightness of the galaxies. Our results are broadly consistent with a scenario in which low surface brightness galaxies follow roughly the same evolutionary history as normal (i.e. high surface) brightness galaxies except at a much lower rate, but require the presence of an initial period of star formation intense enough to allow the formation of massive star clusters.