Ice I
h is the kind you get on Earth under normal conditions, with a hexagonal crystal lattice that forms snowflakes and is less dense than liquid water in the conditions available on Earth. Under specific laboratory conditions and quite probably on other worlds other crystalline phases of water are produced (Ganymede is thought to be mostly made of Ice II). Ice I
c is occasionally known in the upper atmosphere and Ices II-XV have been produced under a range of pressures and temperatures. The water molecules arrange themselves into different structures with different properties.
There's also amorphous ice which lacks any crystalline structure at all.
This is the phase diagram, pressure in Pascals on the y axis, temperature in Kelvin on the x axis.