Optical and near-infrared photometry and optical spectroscopy are reported for SN 2003bg, starting a few days after explosion and extending for a period of more than 300 days. Our early-time spectra reveal the presence of broad, high-velocity Balmer lines. The nebular-phase spectra, on the other hand, show a remarkable resemblance to those of Type Ib/c supernovae, without clear evidence for hydrogen. Near maximum brightness SN 2003bg displayed a bolometric luminosity comparable to that of other Type I hypernovae unrelated to gamma-ray bursts, implying a rather normal amount of 56Ni production (0.1-0.2 Msun) compared with other such objects. The bolometric light curve of SN 2003bg, on the other hand, is remarkably broad, thus suggesting a relatively large progenitor mass at the moment of explosion. These observations, together with the large value of the kinetic energy of expansion established in the accompanying paper (Mazzali et al. 2009), suggest that SN 2003bg can be regarded as a Type IIb hypernova.