The water ice on the three outermost Galilean satellites of Jupiter has a lattice structure that can vary from crystalline to amorphous. Amorphous ice is crystallized by heating, while crystalline ice is amorphized through disruption by particle radiation. We determine ice lattice order using infrared spectra from the Near Infrared Mapping Spectrometer on the Galileo Jupiter orbiter. The shape of the reflectance peak near 3.1 ¿m is diagnostic of the lattice order in the top micrometers of the surface. A narrow, temperature-sensitive band near 1.65 ¿m, from ~1 mm depth, is missing for amorphous ice. Spectral averages of >100 pixels were used for Europa and Callisto, because of high radiation noise and small ice amounts, respectively. Model comparisons show that the surface ice is predominantly amorphous on Europa and predominantly crystalline on Callisto, while both types of ice are found on Ganymede. The distribution of Ganymede ice properties shows a broad global pattern of more amorphous ice in the high-latitude Jovian-facing hemisphere and in the low-latitude trailing hemisphere. The ice at ~1 mm depth on all three satellites is predominantly crystalline. The radiation flux increases by ~300 times between Callisto and Europa, while the thermal crystallization rate may vary over five orders of magnitude among the three satellites (being the fastest at Callisto). The occurrence of crystalline and amorphous ice suggests a balance between the disruption and crystallization, with Callisto dominated by thermal crystallization and Europa by radiative disruption, and with nearly equal rates between the two processes at Ganymede.