We present results from a survey of an unbiased sample of 38 early-type (S0-Sa), low-inclination, optically barred galaxies in the field, using images both from the ground and from space. Our goal was to find and characterize central stellar and gaseous structures: secondary bars, inner disks, and nuclear rings. We find that bars inside bars are surprisingly common: at least one-quarter of the sample galaxies (possibly as many as 40%) are double barred, with no preference for Hubble type or the strength of the primary bar. A typical secondary bar is ~12% of the size of its primary bar and extends to 240-750 pc in radius. Secondary bars are not systematically either parallel or perpendicular to the primary; we see cases where they lead the primary bar in rotation and others where they trail, which supports the hypothesis that the two bars of a double-bar system rotate independently. We see no significant effect of secondary bars on nuclear activity: our double-barred galaxies are no more likely to harbor a Seyfert or LINER nucleus than our single-barred galaxies. We find kiloparsec-scale inner disks in at least 20% of our sample; they occur almost exclusively in S0 galaxies. These disks are on average 20% the size of their host bar and show a wider range of relative sizes than do secondary bars. Nuclear rings are present in about a third of our sample. Most of these rings are dusty, sites of current or recent star formation, or both; such rings are preferentially found in Sa galaxies. Three S0 galaxies (8% of the sample, but 15% of the S0's) appear to have purely stellar nuclear rings, with no evidence for dust or recent star formation. The fact that these central stellar structures are so common indicates that the inner regions of early-type barred galaxies typically contain dynamically cool and disklike structures. This is especially true for S0 galaxies, where secondary bars, inner disks, and/or stellar nuclear rings are present at least two-thirds of the time. If we interpret nuclear rings, secondary bars, and (possibly) inner disks and nuclear spirals as signs of inner Lindblad resonances (ILRs), then between one and two-thirds of barred S0-Sa galaxies show evidence for ILRs.