I always carry the gear needed to fix a flat tire with me, so I haven't for a flat tire.

I have for a frame that broke at the bottom bracket (old schwin rusted out), a cheap walmart bike someone else was riding that busted at the stem, and someone I was riding with didn't have good lighting for night riding and tried to turn into a curb and flatted their tire - they had the gear to fix it but it was only a mile from home so we just walked back as it was easier to fix at home. One time in winter I got picked up biking to my parents place when I found that the last leg of the trail was not plowed at all (it had been plowed up to that point).

I always bring a cell phone and credit card with me in case someone unfixable happens and I need to call a cab. You can't really bring a torch and welding equipment with you in case your frame gives out lol.