"You always need a bit of rope" Sam Gamgee,Lord of the Rings

The thread on ice axes for general walking got me to pondering what items of climbing gear would indeed be useful for "general walking."
Aside from the carabiner used for a keyring, I would say that a "bit of rope," used properly to get over the bumpy parts, would be the most most generally useful.

"used properly" is a key phrase. Used improperly, a rope can mess you up thoroughly, but that is true of many gadgets...

Some of this comes from the time when I worked at Canyon de Chelly, where I soon learned to EDC at least 60 feet of 9mm kernmantle, whether on foot or in a vehicle. We are talking about real climbing rope, not stuff from the hardware store. Never hang from rope from a hardware store.

General skiing -
for towing behind a snowmobile
in case of chairlift evac
short rappels down stream banks

A 50' rope is essential while ice fishing. I keep one in my Otter sled. For this purpose, a lightweight braided nylon rope is sufficient. Might save a life someday, maybe even my own.

As I opened your post, I thought "I wonder what he will say? Surely there is no real use for rope in his flat, lake-infested wilderness..." Just shows how versatile rope can be.

I don't pack rope 'just in case.' Either the full set of climbing gear (helmet, rope harness, etc) or none.

+1. Either we carry proper gear or we avoid needing it.

Proper route planning should determain what you need in advance. Carry a little extra just in case might be needed, but that would be way more then just a rope.

I have also used rope for short canyon hikes to belay my dog up and down exposed sections.

I have used rope for a upstream hand line on below the knee stream crossing to help keep backpackers on their feet on slippery rocks. I wouldn't use it anywhere I wouldn't feel safe crossing without it. It just help keep gear dry. Can also set up a tyrolean for just the gear.

Ice skating we bring an old ice screw too. As well as for an anchor away from shore it also is handy to quickly determine ice depth (it is a long version 9").

"Rope" does not fit with "general walking" for me. It indicates technical or exposed scrambling/climbing. Maybe I'm just getting too old to do that technical stuff much anymore. I have no need for a rope while doing the kind of hiking I do. I carry paracord as part of my emergency gear, but that's not for anticipated technical stuff.

50' of 7mm kermantle in a zip-loc bag, at the bottom of my woods walking day pack. Just-in- case.