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We analyze the global structure of 34 late-type, edge-on, undisturbed, disk galaxies spanning a wide range of mass. We measure structural parameters for the galaxies using two-dimensional least-squares fitting to our $R$-band photometry. The fits require both a thick and a thin disk to adequately fit the data. The thick disks have larger scale heights and longer scale lengths than the embedded thin disks, by factors of ~2 and ~1.25, respectively. The observed structural parameters agree well with the properties of thick and thin disks derived from star counts in the Milky Way and from resolved stellar populations in nearby galaxies. We find that massive galaxies' luminosities are dominated by the thin disk. However, in low mass galaxies (Vc < 120 km/s), thick disk stars contribute nearly half of the luminosity and dominate the stellar mass. Thus, although low mass dwarf galaxies appear blue, the majority of their stars are probably quite old. Our data are most easily explained by a formation scenario where the thick disk is assembled through direct accretion of stellar material from merging satellites while the thin disk is formed from accreted gas. The baryonic fraction in the thin disk therefore constrains the gas-richness of the merging pre-galactic fragments. If we include the mass in HI as part of the thin disk, the thick disk contains <10% of the baryons in high mass galaxies, and ~25-30% of the baryons in low-mass galaxies. We discuss how our trends can be explained by supernova-driven outflow at early times as well as the possibilities for predicting abundance trends in thick disks, and for removing discrepancies between semi-analytic galaxy formation models and the observed colors of low mass galaxies. (abstract abridged)