We present 10.8 mum maps of the central regions of 21 infrared-luminous galaxies. Each map, obtained using the NASA MSFC bolometer array at the IRTF, has a resolution of approximately 4'' and spans typically 25'' x 20''. Some of the galaxies have also been mapped at 12.5, 19.2, and 30 mum. The sample consists primarily of starburst galaxies but includes several Seyferts and LINERs. On average, the flux detected in each map is approximately 58% of that detected at 12 mum by IRAS. We see a variety of morphologies, including compact and elongated sources and more complex distributions exhibiting such features as kiloparsec-size rings and double lobes. The midinfrared radiation is emitted by dust particles, and for two of the galaxies we see spatial color variations attributable to the presence of very small grains and consistent with their depletion in the starbursts. The mid-infrared emission traces the dust heated by the youngest stars. Comparison of the distributions of intense star formation and the dense neutral interstellar medium for eight of these galaxies demonstrates that the two are intimately linked. For several of the galaxies, infrared and CO peaks coincide, although for most of the galaxies the dense gas is much more extended than the star formation. Our sample contains a preponderance of barred galaxies. We show for a subset of the sample that the most intense star formation tends to occur in the circumnuclear regions at the inner Lindblad resonances (ILRs) when ILRs exist or at the nuclei when ILRs do not exist. We interpret these findings by considering how bars and dynamical resonances effect the distribution and properties of gas in galaxies.