Selected area electron diffraction is used to monitor structural changes of vapor-deposited water ice in vacuum during warm-up from 15 to 188 K. A progression of three amorphous forms of water ice is found with well-defined transitions. The formation of a high-density amorphous form (I a h) at 15 K is confirmed, and the transition to the more familiar low-density form (I a l) occurs gradually over the range 38 to 68 K. At 131 K, the ice transforms into a third amorphous form (I a r), which precedes the crystallization of cubic ice (I c ) and coexists metastably with I c from 148 K until at least 188 K. These structural transformations of amorphous water ice can be used to explain hitherto anomalous properties of astrophysical ices. The structural transition from I a h to I a l is responsible for the diffusion and recombination of radicals in ultraviolet-photolyzed interstellar ices at low temperatures. The occurrence and persistence of I a r explains anomalous gas retention and gas release from water-rich ices at temperatures above 150 K.