We present a quantitative measure of the internal color dispersion within galaxies, which quantifies differences in morphology as a function of wavelength. We apply this statistic to a local galaxy sample with archival images at 1500 and 2500 Angstroms from the Ultraviolet Imaging Telescope, and ground-based B-band observations to investigate how the color dispersion relates to global galaxy properties. The intenal color dispersion generally correlates with transformations in galaxy morphology as a function of wavelength, i.e., it quantifies the morphological K-correction. Mid-type spiral galaxies exhibit the highest dispersion in their internal colors, which stems from differences in the bulge, disk, and spiral-arm components. Irregulars and late-type spirals show moderate internal color dispersion, which implies that young stars generally dominate the colors. Ellipticals, lenticulars, and early-type spirals generally have low or negligible internal color dispersion, which indicates that the stars contributing to the UV-to-optical emission have a very homogeneous distribution. We discuss the application of the internal color dispersion to high-redshift galaxies in deep, Hubble Space Telescope images. By simulating local galaxies at cosmological distances, many of the galaxies have luminosities that are sufficiently bright at rest--frame optical wavelengths to be detected within the limits of the currently deepest near-infrared surveys even with no evolution. Under assumptions that the luminosity and color evolution of the local galaxies conform with the measured values of high-redshift objects, we show that galaxies' intrinsic internal color dispersion remains measurable out to z ~ 3. Comment: Accepted for publication in the Astrophysical Journal. 41 pages, 13 figures (3 color). Full resolution version (~8 Mb) available at http://mips.as.arizona.edu/~papovich/papovich_astroph.ps