In reply to Michael MacArthur:
On its own the number of falls a rope is rated to isn't all that useful in determining how safe it is (read the link Johnsulli posted above) but there is a general correlation between that figure and a rope's longevity. The strength of a rope comes from both the core and the sheath but in simplistic terms the core provides the majority of the strength whilst the sheath acts to protect the core from abrasion and sharp edges.
The thicker the sheath the better a rope copes with everyday wear, thin singles (and triple rated ropes) need a strong core to pass the single rope drop tests, but to keep them thin and light they typically have less sheath.
A big fat single rated to take a large number of falls will typically last well because it has a lot of material in the sheath, although the usual disclaimer applies, that any rope may need to be retired after minimal use, possibly just one fall if it gets damaged. Something like the Beal Top Gun II is 10.5mm and rated at 11 falls, or the 10.2mm Mammut Supersafe Evo is rated at 11-12 falls. You can get 11mm ropes rated at 16 or more falls, the sort of thing that is used by climbing walls because thinner ropes would need replacing too frequently. Fat ropes will have a high ratio of sheath to core, but the primary penalty with fat ropes is weight, although they will also be stiffer.
General advice if you want a rope that will last a while (especially if you're working it hard at an indoor wall by falling on it regularly and lowering on it) is to go for at least 10mm, and if you get a rope that is longer than you need you will be able to cut a few metres off the ends when they start to get fuzzy and tired, and still have a useful length left.
