Ever left a bottle of vodka in the freezer for 3 days and discovered small diamond shaped crystals floating in the body of the liquid in a vertical plane? After shaking a bit, the crystals remain in a vertical plane. What's going on here?
The crystals are frozen water - vodka is usually around 40% alcohol and most of the rest is water. The presence of the alcohol lowers the melting point of the liquid as the water molecules are effectively diluted by the alcohol and there is less chance of molecules meeting each other and being able to form the bonds required to make a solid. This is why vodka will not completely freeze at -5 to -20 degrees (freezer temperature). But this doesn't explain the shapes.
Let's start with the basics. As everyone probably knows, the molecules in a solid have little energy and forces between the molecules hold them in a rigid, solid form. As the temperature increases, the molecules gain more energy and therefore vibrate more, breaking the weaker forces holding them together and becoming a liquid. If you give the molecules even more energy they can completely break the forces holding them in a liquid and become a gas. So for a solid to form from a liquid, the molecules must be cooled below their freezing point, allowing bonds between molecules to form and a solid to be made. The formation of ice from water starts with small crystals being formed in the liquid. The water molecules in the liquid surrounding the crystals must then bond to the molecules in the crystals to freeze as well.

Now for why the ice crystals remain in a vertical plane. If you freeze vodka for too long it becomes a bit syrupy. This implies that, although it is still a liquid, the temperature is reduced enough for new bonds to form between molecules and it could be that the ice crystals are held in the vertical plane by these weak forces. Some substances can form what is called a liquid crystal - the molecules are held in roughly parallel layers as is seen in a solid but have enough energy to move around as a liquid would. Interestingly, James Bond asks for Martini, shaken not stirred, because shaking the drink leads to small ice crystals becoming suspended in the liquid which improves the cooling effects of the ice.
The shapes of ice crystals are quite interesting. Water is made up of two hydrogen atoms and an oxygen. Because the oxygen is a bit greedy, it pulls the electrons involved in the bonds with the hydrogens towards itself. This results in the oxygen having a slight negative charge and the hydrogens a slight positive charge (1st picture below). During the formation of a solid, this charge distribution results in a tetrahedral shape (middle picture) that forms a solid with an interlocking hexagon motif. The picture on the right shows the shape taken by a growing ice crystal. New molecules are most likely to bond along a axis where they can form bonds with more than one other molecule. If the molecules were to join along the c axis, they would be forming bonds with just one other molecule as this is a planar surface and these bonds could be overcome more easily.

This explains why ice crystals have hexagonal symmetry - we've
all been told about snowflakes after all. But what about the different
shapes that ice crystals can take, like the diamonds seen in vodka?
Well no one really knows how to explain how different crystals
form, although we do know it has something to do with temperature
and humidity in the case of snowflake formation. Different crystal
shapes include plates, dendrites (snowflakes with long branches),
hollow columns, solid prisms, and needles. For example, the needle
form of ice crystals tends to form at around -20 degrees.
