Only "rescued" twice in 28,000 miles so far.
No.1: Ten miles from home when I sheared a pedal off and phoned the missus for a lift home rather than ride ten miles with only one pedal. She has never forgotten the incident, and has probably told every one of our friends about it since! Next time I'm getting home one legged.
No.2: Heard a ping soon after starting to descend the Col de la Forclaz near Annecy. Watched in horror as my front brake pad flew in an arc to my right and disappeared over the mountainside. Then thirty seconds of panic as I had to apply the front brake metal-on-metal ..... sparks flying from the rim, horrible scraping and juddering and very little noticeable deceleration. A brief inspection of my front wheel when I finally managed to stop (which involved taking some of the rubber off my heels), and there were three distinct metal burrs reminiscent of the initial disastrous attempt at my first year school metalwork project. I started walking downhill .... missing out on a brilliant descent after putting in such an effort on the climb. Riding down that monster was just not an option for a twenty stoner with only one brake. After about a mile, a minibus pulled up and offered a lift down to the valley bottom. I wasn't about to turn it down. It turns out that accepting lifts along mountain roads from mad Austrian minibus drivers can be every bit as scary as cycling down them with missing brakes. I think that guy must have driven the same route several times a day every day of the hang gliding season, and he cut every corner, practically skimmed every cliff face and narrowly avoided every road edge bollard on the way down breaking the speed limit all the way. You know those little grab handles you get in all cars and vans, just above the door .... that you never ever use? Well I used mine that day! My knuckles were white by the time I got out. Should have carried on walking.