This article was originally published here.
You should choose your rope based on intended use.
1. Indoor Climbing

Diameter
Larger diameter (10mm) with a reinforced sheath for intensive outdoor top roping use
Length
Select rope length according to indoor wall's height and profile
Colour
2 colours to choose from to distinguish rope bundles
2. Big Wall Climbing

Diameter
Larger diameter ropes (10mm) last longer and are safer to use (better braking in the device). They are recommended for beginners. Smaller diameter ropes are lighter and more fluid, but they require higher skill level. Smallest diameter ropes should be used by expert climbers.

Length
Select rope length according to big wall's height and profile
3. Multi Pitch Climbing, Mountaineering And Ice Climbing

Diameter
Double ropes are used for abseiling after climbing. 2 diameters exist. A thinner rope will be lighter but less durable and its use will require expert belaying technique.
Length
Select rope length according to length of route and abseil
Colour
Double ropes come in 2 colours for extra safety
4. Glacier Hiking

Diameter
A single very thin diameter for lower weight

Length
Select rope length according to the number of persons on the rope : 20m, 30m, 40m