We have initiated a search for extended ultraviolet disk (XUV-disk) galaxies in the local universe. Herein, we compare GALEX UV and visible--NIR images of 189 nearby (D$<$40 Mpc) S0--Sm galaxies included in the GALEX Atlas of Nearby Galaxies and present the first catalogue of XUV-disk galaxies. We find that XUV-disk galaxies are surprisingly common but have varied relative (UV/optical) extent and morphology. Type~1 objects ($\ga$20% incidence) have structured, UV-bright/optically-faint emission features in the outer disk, beyond the traditional star formation threshold. Type~2 XUV-disk galaxies ($∼$10% incidence) exhibit an exceptionally large, UV-bright/optically-low-surface-brightness (LSB) zone having blue $UV-K_s$ outside the effective extent of the inner, older stellar population, but not reaching extreme galactocentric distance. If the activity occuring in XUV-disks is episodic, a higher fraction of present-day spirals could be influenced by such outer disk star formation. Type~1 disks are associated with spirals of all types, whereas Type~2 XUV-disks are predominantly found in late-type spirals. Type~2 XUV-disks are forming stars quickly enough to double their [presently low] stellar mass in the next Gyr (assuming a constant SF rate). XUV-disk galaxies of both types are systematically more gas-rich than the general galaxy population. Minor external perturbation may stimulate XUV-disk incidence, at least for Type~1 objects. XUV-disks are the most actively evolving galaxies growing via inside-out disk formation in the current epoch, and may constitute a segment of the galaxy population experiencing significant, continued gas accretion from the intergalactic medium or neighboring objects.