The ASAS-SN Bright Supernova Catalog -- III. 2016

This catalog summarizes information for all supernovae discovered by the All-Sky Automated Survey for SuperNovae (ASAS-SN) and all other bright ($m_{peak}leq17$), spectroscopically confirmed supernovae discovered in 2016. We then gather the near-IR through UV magnitudes of all host galaxies and the offsets of the supernovae from the centers of their hosts from public databases. We illustrate the results using a sample that now totals 668 supernovae discovered since 2014 May 1, including the supernovae from our previous catalogs, with type distributions closely matching those of the ideal magnitude limited sample from Li et al. (2011). This is the third of a series of yearly papers on bright supernovae and their hosts from the ASAS-SN team.