In this paper, we present mid-infrared spectra of a comprehensive set of Herbig Ae/Be stars observed with the Spitzer Space Telescope. The signal-to-noise ratio of these spectra is very high, ranging between about a hundred and several hundreds. During the analysis of these data we tested the validity of standardized protoplanetary dust models and studied grain growth and crystal formation. On the basis of the analyzed spectra, the major constituents of protoplanetary dust around Herbig Ae/Be stars are amorphous silicates with olivine and pyroxene stoichiometry, crystalline forsterite, and enstatite and silica. No other solid-state features, indicating other abundant dust species, are present in the Spitzer spectra. Deviations of the synthetic spectra from the observations are most likely related to grain shape effects and uncertainties in the iron content of the dust grains. Our analysis revealed that larger grains are more abundant in the disk atmosphere of flatter disks than in that of flared disks, indicating that grain growth and sedimentation decrease the disk flaring. We did not find, however, correlations between the value of crystallinity and any of the investigated system parameters. Our analysis shows that enstatite is more concentrated toward the warm inner disk than forsterite, in contrast to predictions of equilibrium condensation models. None of the three crystal formation mechanisms proposed so far can alone explain all our findings. It is very likely that all three play at least some role in the formation of crystalline silicates.