The origin of S0 galaxies is discussed in the framework of early mergers in a cold dark matter cosmology, and in a scenario where S0s are assumed to be former spirals stripped of gas. From an analysis of 127 early-type disk galaxies (S0-Sa), we find a clear correlation between the scale parameters of the bulge (r(eff)) and the disk (h(R)), a correlation which is difficult to explain if these galaxies were formed in mergers of disk galaxies. However, the stripping hypothesis, including quiescent star formation, is not sufficient to explain the origin of S0s either, because it is not compatible with our finding that S0s have a significantly smaller fraction of bars (46% +/- 6%) than their assumed progenitors, S0/a galaxies (93% +/- 5%) or spirals (64%-69%). Our conclusion is that even if a large majority of S0s were descendants of spiral galaxies, bars and ovals must play an important role in their evolution. The smaller fraction particularly of strong bars in S0 galaxies is compensated by a larger fraction of ovals/lenses (97% +/- 2% compared to 82%-83% in spirals), many of which might be weakened bars. We also found massive disklike bulges in nine of the S0 galaxies, which might have formed at an early gas-rich stage of galaxy evolution.