We have carried out mid-infrared spectroscopy of seven Galactic proto-planetary nebulae (PPNs) using the Spitzer Space Telescope. They were observed from 10-36 microns at relatively high spectral resolution, R~600. The sample was chosen because they all gave some evidence in the visible of a carbon-rich chemistry. All seven of the sources show the broad, unidentified 21 micron emission feature; three of them are new detections (IRAS 06530-0213, 07430+1115, and 19477+2401) and the others are observed at higher S/N than in previous spectra. These have the same shape and central wavelength (20.1 microns) as found in the ISO spectra of the brighter PPNs. The 30 micron feature was seen in all seven objects. However, it is not resolved into two separate features (26 and 33 microns) as was claimed on the basis of ISO spectra, which presumably suffered from the noisy detector bands in this region. All showed the infrared aromatic bands (AIB) at 11.3, 12.4, and 13.3 microns. Five of these also appear to have the C2H2 molecular band at 13.7 microns, one in absorption and four in emission. This is extremely rare, with only one other evolved star, IRC+10216, in which C2H2 emission has been observed. Four also possessed a broad, unidentified emission feature at 15.8 microns that may possibly be related to the 21 micron feature. Model fits were made to the spectral energy distributions for these PPNs to determine properties of the detached circumstellar envelopes. The 21 micron feature has been seen in all Galactic carbon-rich PPNs observed, and thus its carrier appears to be a common component of the outflow around these objects.