Years ago, I did archeological field work in Canyon de Chelly, Arizona, and spent a lot of time hiking there. A lot of the trails were rock scrambles, using toe and hand routes of various ages, and it was very easy to get off route and suffer various other adventures. I developed the practice of ALWAYS carrying a 60 foot length of 3/8" (9mm)climbing rope - more of courseif I was planning to do some climbing. It came in handy several times - didn't weigh much and took up very little space in my pack. Used it for rappels, a very modest amount of impromptu leading, and also to give a belay to companions who were bothered by the considerable exposure on some of the "trails."

I would recommend something similar if venturing into rough country, provided you have the knowledge to use the rope properly. Rappeling is as dangerous as lead climbing, and it is often difficult/impossible to reverse a rappel, unlike a pitch you have climbed.

I wouldn't go any thinner than 3/8 because I carried only the rope, and body rappeled, if a rap was called for. That way I avoided the considerable weight and bulk of harness and descender, etc. A thinner rope, used for a body rappel, would cut far too much.

I think it was Sam Gamgee who said, "You always need a little bit of rope" - LOTR