I've had two in really remote places. Once I rode 10 km on a rear flat, intentionally ruining a rim. The second time I broke a chain 20 km from civilization and had to persuade the one vehicle that passed to turn around and take me back to town (Dili, East Timor). I've called the wife a couple of times: once for an unrideable wheel and once for a bloody crash (laid the bike down on a mountain curve when an oncoming vehicle crossed the double yellow.

Now I mostly rescue others. I carry a small chain pin tool, spare pins, spare connex links, a tube, a tire boot, vulcanizing patch kit, pump, spoke wrenches, etcetera. It's not a lot of bulk. The pump straps to the bike and everything else fits in a jersey pocket. Short of catastrophic failure I can make a bike rideable with this kit.