To study the physical and chemical evolution of ices in solar-mass systems, a spectral survey is conducted of a sample of 41 low-luminosity YSOs (L similar to 0.1-10 L-circle dot) using 3-38 mu m Spitzer and ground-based spectra. The sample is complemented with previously published Spitzer spectra of background stars and with ISO spectra of well-studied massive YSOs (L similar to 10(5) L-circle dot). The long-known 6.0 and 6.85 mu m bands are detected toward all sources, with the Class 0-type YSOs showing the deepest bands ever observed. The 6.0 mu m band is often deeper than expected from the bending mode of pure solid H2O. The additional 5-7 mu m absorption consists of five independent components, which, by comparison to laboratory studies, must be from at least eight different carriers. Much of this absorption is due to simple species likely formed by grain surface chemistry, at abundances of 1%-30% for CH3OH, 3%-8% for NH3, 1%-5% for HCOOH, similar to 6% for H2CO, and similar to 0.3% for HCOO- relative to solid H2O. The 6.85 mu m band has one or two carriers, of which one may be less volatile than H2O. Its carrier(s) formed early in the molecular cloud evolution and do not survive in the diffuse ISM. If an NH4+- containing salt is the carrier, its abundance relative to solid H2O is similar to 7%, demonstrating the efficiency of low-temperature acid-base chemistry or cosmic-ray-induced reactions. Possible origins are discussed for enigmatic, very broad absorption between 5 and 8 mu m. Finally, the same ices are observed toward massive and low-mass YSOs, indicating that processing by internal UV radiation fields is a minor factor in their early chemical evolution.