We present results of the first unbiased search for extended ultraviolet (XUV)-disk galaxies undertaken to determine the space density of such galaxies. Our sample contains 561 local (0.001<z<0.05) galaxies that lie in the intersection of available Galaxy Evolution Explorer (GALEX) deep imaging (exposure time >1.5x10^4^s) and Sloan Digital Sky Survey DR7 footprints. We explore modifications to the standard classification scheme for our sample that includes both disk- and bulge-dominated galaxies. Visual classification of each galaxy in the sample reveals an XUV-disk frequency of up to 20% for the most nearby portion of our sample. On average over the entire sample (out to z=0.05) the frequency ranges from a hard limit of 4%-14%. The GALEX imaging allows us to detect XUV disks beyond 100 Mpc. The XUV regions around XUV-disk galaxies are consistently bluer than the main bodies. We find a surprisingly high frequency of XUV emission around luminous red (NUV-r>5) and green valley (3<NUV-r<5) galaxies. The XUV-disk space density in the local universe is >(1.5-4.2)x10^-3^Mpc^-3^. Using the XUV emission as an indicator of recent gas accretion, we estimate that the cold gas accretion rate onto these galaxies is >(1.7-4.6)x10^-3^M_{sun}_/Mpc^3^/yr. The number of XUV disks in the green valley and the estimated accretion rate onto such galaxies points to the intriguing possibility that 7%-18% of galaxies in this population are transitioning away from the red sequence.