What causes faults in the Earth's crust?
The plates of the Earth's crust sit on a 'sea' of molten magma. The convection within the magma causes these plates to move - it is the energy release of this movement that causes faults. It should be noted that faults are usually not a single 'clean cut' and the area of a fault is more often termed 'fault zone'.
Plate techtonics can exist because of the internal heat of the Earth's core. For smaller planets, Mars for example, the core has cooled and the magma as 'set'. As a result the plates (or thin flakey crust in the example of Mars) can no longer move - there are no Earthquakes and volcanoes are extinct.
There are several types of faults, each described by the movement of the interacting plates: strike-slip, dip-slip, oblique-slip (a combination of the previous two types), listric (curved) and ring.