Small organic molecules, such as C2H, HCN, and H2CO, are tracers of the C, N, and O budget in protoplanetary disks. We present high-angular-resolution (10-50 au) observations of C2H, HCN, and H2CO lines in five protoplanetary disks from the Molecules with ALMA at Planet-forming Scales (MAPS) ALMA Large Program. We derive column density and excitation temperature profiles for HCN and C2H, and find that the HCN emission arises in a temperate (20-30 K) layer in the disk, while C2H is present in relatively warmer (20-60 K) layers. In the case of HD 163296, we find a decrease in column density for HCN and C2H inside one of the dust gaps near ~83 au, where a planet has been proposed to be located. We derive H2CO column density profiles assuming temperatures between 20 and 50 K, and find slightly higher column densities in the colder disks around T Tauri stars than around Herbig Ae stars. The H2CO column densities rise near the location of the CO snowline and/or millimeter dust edge, suggesting an efficient release of H2CO ices in the outer disk. Finally, we find that the inner 50 au of these disks are rich in organic species, with abundances relative to water that are similar to cometary values. Comets could therefore deliver water and key organics to future planets in these disks, similar to what might have happened here on Earth. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.