We have observed a sample of 35 long-period variables and four Cepheid variables in the vicinity of 23 Galactic globular clusters using the Infrared Spectrograph on the Spitzer Space Telescope. The long-period variables in the sample cover a range of metallicities from near solar to about 1/40th solar. The dust mass-loss rate from the stars increases with pulsation period and bolometric luminosity. Higher mass-loss rates are associated with greater contributions from silicate grains. The dust mass-loss rate also depends on metallicity. The dependence is most clear when segregating the sample by dust composition, less clear when segregating by bolometric magnitude, and absent when segregating by period. The spectra are rich in solid-state and molecular features. Emission from alumina dust is apparent across the range of metallicities. Spectra with a 13-um dust emission feature, as well as an associated feature at 20 um, also appear at most metallicities. Molecular features in the spectra include H_2O bands at 6.4-6.8 um, seen in both emission and absorption, SO_2 absorption at 7.3-7.5 um, and narrow emission bands from CO_2 from 13.5 to 16.8 um. The star Lynga 7 V1 has an infrared spectrum revealing it to be a carbon star, adding to the small number of carbon stars associated with Galactic globular clusters.