I know this one at first would normally make no sense, but as my neighbor found out today, the worst possible time to find out your emergency brake isn't working is on a small incline while trying to change a flat tire. He has a 2005 dodge crew cab 4x4, and today, he got a flat on the rear, on a small uphill incline, so he pulled over, put his truck in park, set the e-brake, and proceeded to jack his truck up, but everytime the wheel would be just about off the ground, the truck would want to roll down the hill on him, so, he decided to drive very slowly on the side of the road, until he could get to a flat spot and change the tire.
After moving the truck, he realized the e-brake was on the whole time, from when he set it the first time, and seemed to not be doing anything at all to stop the truck. After changing the tire, he went to a local shop that does free brake inspections, and they informed him that his e-brake shoes were shot. After talking to him about it, i had a thought. Why not carry a short pair of 4x4 wood blocks, that way you have a backup to block the wheels, and not have to be worried about your vehicle rolling away on you. i know the best solution is always make sure the e-brake works, but, at least in NY and PA, they are supposed to check that at inspection time, so most people i know don't bother checking it themselves, myself included sometimes.
Another place i see where this would be useful, is an incident i witnessed about a year ago. I was on the highway, and there was a guy towing a rather large boat, and for some reason he was stopped about halfway up the side of an incline, that was maybe half a mile long, and was changing, or rather trying to change a flat on his truck, but, because either his e-brake didn't work properly, or the weight of the boat was too much for the e-brake, the truck wanted to slide itself down the hill. He ultimately had to drive almost a mile, to where he could safely change the tire, but even then, his wife was in the truck with her foot on the brake, just in case.