I guess I'm old school...
So much so that I'm nervous setting out on the smallest trips without a full-sized spare tire. A flat is dangerous enough, and being without a quick and somewhat easy way to remedy it and be on my way could also be dangerous depending on where you are.
The only time I can ever recall needing a spare tire on the road was back several years when I had the Budget Zagato. I was heading to my friend Val's shop on the Olympic peninsula via SR101. Some distance up the road, about a 1.5 hour drive, I encountered a football sized rock in the road. The weather was drizzly so I tried to straddle it but caught the edge with one of the rear wheels. I stopped at the next opportunity to survey the damage and sure enough the rock bent the wheel and damaged the side of the tire, which went flat as I watched it.
I changed the tire and eventually got back on the road. Given the remoteness of the area, it may have been impossible to call AAA, which I carry. I've been on other back road drives and have always felt safer with a full sized spare. I carry a 12v tire pump as well, but do try to keep the spare aired up.