I have carried a foldable spare tire, and like much of what I now carry when touring, it is because of something that happened in the past.
One afternoon while on tour my rear rack failed at the seat post braze-on. The rack, still attached at the hub braze-on, slid down the rear tire and began scrapping against the pavement. The slide down the tire took about 10 inches of rubber off the tire. It did not expose the tube, but there was not much between the tube and the road. I was able to limp into the nearest town, which was about 12 miles away. This small town did not have any bike tires, but I did find a glue that is used on tennis shoes that I used to layer over the tire gash. Layer by layer (it took me a number of hours because each layer had to dry before I could add another). The nearest town with available bike tires was about 65 miles away. That shoe-gu stuff lasted for about 40 miles, then I began having flat after flat. I had to walk into a town that was about 20 miles from the town where I could obtain a tire. I called the bike shop and they delivered the tire, for a hefty fee.
After that mishap, beside obtaining a new rear rack, I began carrying a foldable spare if my route was to take me where services were spotty. I did that for a number of tours, but I haven't carried a spare for the last several years.
Another tour mishap is also why I carry four spare tubes. Overkill, yes, but it gives me peace of mind, and it doesn't weigh that much.
