First off, there are static and dynamic ropes.
Static ropes do not stretch and are mostly used for rappelling, hauling, fixed lines, and probably some other stuff I do not know about. This is because none of these activities involve large forces - such as what would be created during a fall.
Dynamic ropes stretch, and are the main type of rope used for rock climbing. This is because they stretch to absorb the shock of the climbing rope. In fact, if I remember correctly, some rock climbing ropes can stretch to as much as 30% more than it's original length.
Dynamic ropes come in a wide range of diameters and can also be divided into three categories - single ropes, half ropes, and twin ropes. One would choose a certain diameter and type of rope based on the activity they plan on doing.
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