We construct a large data set of global structural parameters for 1300 field and cluster spiral galaxies and explore the joint distribution of luminosity L, optical rotation velocity V, and disk size R at I- and 2MASS K-bands. The I- and K-band velocity-luminosity (VL) relations have log-slopes of 0.29 and 0.27, respectively with sigma_ln(VL)~0.13, and show a small dependence on color and morphological type in the sense that redder, early-type disk galaxies rotate faster than bluer, later-type disk galaxies for most luminosities. The VL relation at I- and K-bands is independent of surface brightness, size and light concentration. The log-slope of the I- and K-band RL relations is a strong function of morphology and varies from 0.25 to 0.5. The average dispersion sigma_ln(RL) decreases from 0.33 at I-band to 0.29 at K, likely due to the 2MASS selection bias against lower surface brightness galaxies. Measurement uncertainties are sigma_ln(V)~0.09, sigma_ln(L)~0.14 and somewhat larger and harder to estimate for ln(R). The color dependence of the VL relation is consistent with expectations from stellar population synthesis models. The VL and RL residuals are largely uncorrelated with each other; the RV-RL residuals show only a weak positive correlation. These correlations suggest that scatter in luminosity is not a significant source of the scatter in the VL and RL relations. The observed scaling relations can be understood in the context of a model of disk galaxies embedded in dark matter halos that invokes low mean spin parameters and dark halo expansion, as we describe in our companion paper (Dutton et al. 2007). We discuss in two appendices various pitfalls of standard analytical derivations of galaxy scaling relations, including the Tully-Fisher relation with different slopes. (Abridged).
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