Spitzer Space Telescope observations of 15 spiral galaxies show numerous dense cores at 8{mu}m that are revealed primarily in unsharp mask images. The cores are generally invisible in optical bands because of extinction, and they are also indistinct at 8{mu}m alone because of contamination by more widespread diffuse emission. Several hundred core positions, magnitudes, and colors from the four InfraRed Array Camera bands are measured and tabulated for each galaxy. The larger galaxies, which tend to have longer and more regular spiral arms, often have their infrared cores aligned along these arms, with additional cores in spiral arm spurs. Galaxies without regular spirals have their cores in more irregular spiral-like filaments, with typically only one or two cores per filament. Nearly every elongated emission feature has 8{mu}m cores strung out along its length. The occurrence of dense cores in long and thin filaments is reminiscent of filamentary star formation in the solar neighborhood, although on a scale 100 times larger in galaxies. The cores most likely form by gravitational instabilities and cloud agglomeration in the filaments. The simultaneous occurrence of several cores with regular spacings in some spiral arms suggests that in these cases, all of the cores formed at about the same time and the corresponding filaments are young. Total star formation rates for the galaxies correlate with the total embedded stellar masses in the cores with an average ratio corresponding to a possible age between 0.2 and 2Myr. This suggests that the identified cores are the earliest phase for most star formation.