We measure the star formation efficiency (SFE), the star formation rate per unit gas, in 23 nearby galaxies and compare it to expectations from proposed star formation laws and thresholds. We use HI maps from THINGS and derive H2 maps from HERACLES and BIMA SONG CO. We estimate the star formation rate by combining GALEX FUV maps and SINGS 24 micron maps, infer stellar surface density profiles from SINGS 3.6 micron data, and use kinematics from THINGS. We measure the SFE as a function of: the free-fall and orbital timescales; midplane gas pressure; stability of the gas disk to collapse (including the effects of stars); the ability of perturbations to grow despite shear; and the ability of a cold phase to form. In spirals, the SFE of H2 alone is nearly constant at 5.25 +/- 2.5 x 10^(-10) yr^(-1) (equivalent to an H2 depletion time of 1.9x10^9 yr) as a function of all of these variables at our 800 pc resolution. Where the ISM is mostly HI, on the other hand, the SFE decreases with increasing radius in both spiral and dwarf galaxies, a decline reasonably described by an exponential with scale length 0.2-0.25 r_25. We interpret this decline as a strong dependence of GMC formation on environment. The ratio of H2 to HI appears to be a smooth function of radius, stellar surface density, and pressure spanning from the H2-dominated to HI-dominated ISM. The radial decline in SFE is too steep to be reproduced only by increases in the free-fall time or orbital time. Thresholds for large-scale instability suggest that our disks are stable or marginally stable and do not show a clear link to the declining SFE. We suggest that ISM physics below the scales that we observe - phase balance in the HI, H2 formation and destruction, and stellar feedback - governs the formation of GMCs from HI.
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