Y dwarfs provide a unique opportunity to study free-floating objects with masses <30M_Jup_ and atmospheric temperatures approaching those of known Jupiter-like exoplanets. Obtaining distances to these objects is an essential step toward characterizing their absolute physical properties. Using Spitzer's Infrared Array Camera (IRAC) [4.5] images taken over baselines of ~2-7yrs, we measure astrometric distances for 22 late-T and early Y dwarfs, including updated parallaxes for 18 objects and new parallax measurements for 4 objects. These parallaxes will make it possible to explore the physical parameter space occupied by the coldest brown dwarfs. We also present the discovery of six new late-T dwarfs, updated spectra of two T dwarfs, and the reclassification of a new Y dwarf, WISE J033605.04-014351.0, based on Keck/NIRSPEC J-band spectroscopy. Assuming that effective temperatures are inversely proportional to absolute magnitude, we examine trends in the evolution of the spectral energy distributions of brown dwarfs with decreasing effective temperature. Surprisingly, the Y dwarf class encompasses a large range in absolute magnitude in the near- to mid-infrared photometric bandpasses, demonstrating a larger range of effective temperatures than previously assumed. This sample will be ideal for obtaining mid-infrared spectra with the James Webb Space Telescope because their known distances will make it easier to measure absolute physical properties.