This paper is one in a series presenting results obtained within the Formation and Evolution of Planetary Systems (FEPS) Legacy Science Program on the Spitzer Space Telescope. Here we present a study of dust processing and growth in seven protoplanetary disks. Our spectra indicate that the circumstellar silicate dust grains have grown to sizes at least 10 times larger than observed in the interstellar medium and show evidence for a non-negligible (similar to 5% in mass fractions) contribution from crystalline species. These results are similar to those of other studies of protoplanetary disks. In addition, we find a correlation between the strength of the amorphous silicate feature and the shape of the spectral energy distribution. This latter result is consistent with the growth and subsequent gravitational settling of dust grains toward the disk midplane. Furthermore, we find a change in the relative abundance of the different crystalline species: more enstatite than forsterite is observed in the inner warm dust population at similar to 1 AU, while forsterite dominates in the colder outer regions at similar to 5-15 AU. This change in the relative abundances argues for a localized crystallization process rather than a radial mixing scenario in which crystalline silicates are being transported outwards from a single formation region in the hot inner parts of the disk. Finally, we report the detection of emission from polycyclic aromatic hydrocarbon ( PAH) molecules in five out of seven sources. We find a tentative PAH band at 8.2 mu m that was previously undetected in the spectra of disks around low-mass pre-main-sequence stars.