It has been implicitly assumed that ices on grains in molecular clouds and protoplanetary disks are formed by homogeneous layers regardless of their composition or crystallinity. To verify this assumption, we observed the H2O deposition onto refractory substrates and the crystallization of amorphous ices (H2O, CO2, and CO) using an ultra-high-vacuum transmission electron microscope. In the H2O-deposition experiments, we found that three-dimensional islands of crystalline ice (Ic) were formed at temperatures above 130 K. The crystallization experiments showed that uniform thin films of amorphous CO and H2O became three-dimensional islands of polyhedral crystals; amorphous CO2, on the other hand, became a thin film of nano-crystalline CO2 covering the amorphous H2O. Our observations show that crystal morphologies strongly depend not only on the ice composition but also on the substrate. Using experimental data concerning the crystallinity of deposited ices and the crystallization timescale of amorphous ices, we illustrated the criteria for ice crystallinity in space and outlined the macroscopic morphology of icy grains in molecular clouds as follows: amorphous H2O covered the refractory grain uniformly, CO2 nano-crystals were embedded in the amorphous H2O, and a polyhedral CO crystal was attached to the amorphous H2O. Furthermore, a change in the grain morphology in a protoplanetary disk is shown. These results have important implications for the chemical evolution of molecules, nonthermal desorption, collision of icy grains, and sintering.