We present azimuthally averaged radial profiles of R-band surface brightness for a complete sample of 47 early-type, unbarred galaxies, as a complement to our previous study of early-type barred galaxies. Following very careful sky subtraction, the profiles can typically be determined down to brightness levels well below 27 mag arcsec-2 and in the best cases below 28 mag arcsec-2. We classified the profiles according to the scheme used previously for the barred sample: Type I profiles are single unbroken exponential radial declines in brightness; Type II profiles ("truncations") have an inner shallow slope (usually exponential) which changes at a well-defined break radius to a steeper exponential; and Type III profiles ("antitruncations") have an inner exponential that is steeper, giving way to a shallower outer (usually exponential) decline. By combining these profiles with previous studies, we can make the first clear statements about the trends of outer-disk-profile types along the Hubble sequence (including both barred and unbarred galaxies), and their global frequencies. We find that Type I profiles are most frequent in early-type disks, decreasing from one-third of all S0-Sa disks to barely 10% of the latest-type spirals. Conversely, Type II profiles (truncations) increase in frequency with Hubble type, from only ~25% of S0 galaxies to ~80% of Sd-Sm spirals. Overall, the fractions of Type I, II, and III profiles for all disk galaxies (Hubble types S0-Sm) are 21%, 50%, and 38%, respectively; this includes galaxies (~8% of the total) with composite Type II+III profiles (counted twice). Finally, we note the presence of bars in 10 galaxies previously classified (optically) as "unbarred." This suggests that ~20% of optically unbarred galaxies are actually barred; the bars in such cases can be weak, obscured by dust, or so large as to be mistaken for the main disk of the galaxy.