We have obtained milliarcsecond-scale spectral index distributions for a sample of 190 extragalactic radio jets through the Monitoring of Jets in Active Galactic Nuclei with the VLBA Experiments (MOJAVE) project. We use the spectral index maps to study the spectral index evolution along the jet and determine the spectral distributions in different locations of the jets. The overall jet spectrum steepens at a rate of about -0.001 to -0.004 per deprojected parsec when moving further out from the core with flat spectrum radio quasars having significantly steeper spectra (mean -1.09 + or - 0.04) than the BL Lac objects (mean -0.80 + or - 0.05). We find a significant trend that jet components with linear polarization parallel to the jet (magnetic field perpendicular to the jet) have flatter spectra, as expected for transverse shocks. This interpretation is supported by a significant correlation with the age of the component and the spectral index, with older components having steeper spectra.