Rings are the most frequently revealed substructure in Atacama Large Millimeter/submillimeter Array (ALMA) dust observations of protoplanetary disks, but their origin is still hotly debated. In this paper, we identify dust substructures in 12 disks and measure their properties to investigate how they form. This subsample of disks is selected from a high-resolution (∼0.″12) ALMA 1.33 mm survey of 32 disks in the Taurus star-forming region, which was designed to cover a wide range of brightness and to be unbiased to previously known substructures. While axisymmetric rings and gaps are common within our sample, spiral patterns and high-contrast azimuthal asymmetries are not detected. Fits of disk models to the visibilities lead to estimates of the location and shape of gaps and rings, the flux in each disk component, and the size of the disk. The dust substructures occur across a wide range of stellar mass and disk brightness. Disks with multiple rings tend to be more massive and more extended. The correlation between gap locations and widths, the intensity contrast between rings and gaps, and the separations of rings and gaps could all be explained if most gaps are opened by low-mass planets (super-Earths and Neptunes) in the condition of low disk turbulence (α = 10-4). The gap locations are not well correlated with the expected locations of CO and N2 ice lines, so condensation fronts are unlikely to be a universal mechanism to create gaps and rings, though they may play a role in some cases.