We report the discovery of spiral galaxies that are as optically luminous as elliptical brightest cluster galaxies, with r-band monochromatic luminosity Lr = 8-14L* (4.3-7.5 × 1044 erg s-1). These super spiral galaxies are also giant and massive, with diameter D = 57-134 kpc and stellar mass Mstars = 0.3-3.4 × 1011M☉. We find 53 super spirals out of a complete sample of 1616 SDSS galaxies with redshift z < 0.3 and Lr > 8L*. The closest example is found at z = 0.089. We use existing photometry to estimate their stellar masses and star formation rates (SFRs). The SDSS and Wide-field Infrared Survey Explorer colors are consistent with normal star-forming spirals on the blue sequence. However, the extreme masses and rapid SFRs of 5-65 M☉ yr-1 place super spirals in a sparsely populated region of parameter space, above the star-forming main sequence of disk galaxies. Super spirals occupy a diverse range of environments, from isolation to cluster centers. We find four super spiral galaxy systems that are late-stage major mergers—a possible clue to their formation. We suggest that super spirals are a remnant population of unquenched, massive disk galaxies. They may eventually become massive lenticular galaxies after they are cut off from their gas supply and their disks fade.