We measure the relation between galaxy luminosity and disk circular velocity (the Tully-Fisher TF relation), in the g, r, i, and z-bands, for a broadly selected sample of galaxies from the Sloan Digital Sky Survey, with the goal of providing well defined observational constraints for theoretical models of galaxy formation. The input sample of 234 galaxies has a roughly flat distribution of absolute magnitudes in the range -18.5 > Mr > -22, and our only morphological selection is an axis-ratio cut b/a < 0.6 to allow accurate inclination corrections. Long-slit spectroscopy yields usable H-alpha rotation curves for 162 galaxies. Observational errors, including distance errors due to peculiar velocities, are small compared to the intrinsic scatter of the TF relation. The slope of the forward TF relation steepens from -5.5 +/- 0.2 mag/log(km/s) in the g-band to -6.6 +/- 0.2 mag/log(km/s) in the z-band. The intrinsic scatter is approximately 0.4 mag in all bands. The scatter is not dominated by rare outliers or by any particular class of galaxies, though it drops slightly, to 0.36 mag, if we restrict the sample to nearly bulgeless systems. Correlations of TF residuals with other galaxy properties are weak: bluer galaxies are significantly brighter than average in the g-band but only marginally brighter in the i-band; more concentrated galaxies are slightly fainter than average; and the TF residual is virtually independent of half-light radius, contrary to the trend expected for gravitationally dominant disks. The observed residual correlations do not account for most of the intrinsic scatter, implying that this scatter is instead driven largely by variations in the ratio of dark to luminous matter within the disk galaxy population.