Spiral galaxies range from bulge-dominated early-type galaxies to late types with little or no bulge. Cosmological models do not predict the formation of disk-dominated, essentially bulgeless galaxies, yet these objects exist. A particularly striking and poorly understood example of bulgeless galaxies are flat or superthin galaxies with large axis ratios. We therefore embarked on a study aimed at a better understanding of these enigmatic objects, starting by compiling a statistically meaningful sample with well-defined properties. The disk axis ratios can be most easily measured when galaxies are seen edge-on. We used data from the Sloan Digital Sky Survey (SDSS) in order to identify edge-on galaxies with disks in a uniform, reproducible, automated fashion. In the five-color photometric database of the SDSS Data Release 1 (2099 deg2) we identified 3169 edge-on disk galaxies, which we subdivided into disk galaxies with bulge, intermediate types, and simple disk galaxies without any obvious bulge component. We subdivided these types further into subclasses: Sa(f), Sb(f), Sc(f), Scd(f), Sd(f), Irr(f), where the (f) indicates that these galaxies are seen edge-on. Here we present our selection algorithm and the resulting catalogs of the 3169 edge-on disk galaxies including the photometric, morphological, and structural parameters of our targets. A number of incompleteness effects affect our catalog, but it contains almost a factor of four more bulgeless galaxies with prominent simple disks (flat galaxies) within the area covered here than previous optical catalogs, which were based on the visual selection from photographic plates (cf. Karachentsev et al. 1999, Bull. Special Astrophys. Obs., 47, 5). We find that approximately 15% of the edge-on disk galaxies in our catalog are flat galaxies, demonstrating that these galaxies are fairly common, especially among intermediate-mass star-forming galaxies. Bulgeless disks account for roughly one third of our galaxies when also puffy disks and edge-on irregulars are included. Our catalog provides a uniform database for a multitude of follow-up studies of bulgeless galaxies in order to constrain their intrinsic and environmental properties and their evolutionary status.