We present 161 Spitzer Infrared Spectrograph (IRS) spectra of T Tauri stars and young brown dwarfs in the Taurus star-forming region. All of the targets were selected based on their infrared excess and are therefore surrounded by protoplanetary disks; they form the complete sample of all available IRS spectra of T Tauri stars with infrared excesses in Taurus. We also present the IRS spectra of seven Class 0/I objects in Taurus to complete the sample of available IRS spectra of protostars in Taurus. We use spectral indices that are not significantly affected by extinction to distinguish between envelope- and disk-dominated objects. Together with data from the literature, we construct spectral energy distributions for all objects in our sample. With spectral indices derived from the IRS spectra we infer disk properties such as dust settling and the presence of inner disk holes and gaps. We find a transitional disk frequency, which is based on objects with unusually large 13-31 μm spectral indices indicative of a wall surrounding an inner disk hole, of about 3%, and a frequency of about 20% for objects with unusually large 10 μm features, which could indicate disk gaps. The shape and strength of the 10 μm silicate emission feature suggests weaker 10 μm emission and more processed dust for very low mass objects and brown dwarfs (spectral types M6-M9). These objects also display weaker infrared excess emission from their disks, but do not appear to have more settled disks than their higher-mass counterparts. We find no difference for the spectral indices and properties of the dust between single and multiple systems.