Sorry, but for a properly maintained bicycle, punctures are far and away the most common problem you will encounter on the road. In my own case, I have not even had a puncture for more than 3 years. I will enumerate some of the (rare) problems I have had. Broken spokes: they happen, but often do not stop you from finishing your ride. I even finished a race once with a broken spoke and had a good result. Chains: I have never broken one on a ride, maybe because I don't let them wear out. I once had to cut a ride short because the cleat for my clipless pedal broke. Didn't want to make my ride companions have to wait for me. I had a rear wheel lock up due to a maintenance issue once in 20 years of commuting. My own fault. The main point is, if you take proper care of your bicycle, flat tires are your biggest problem, and even then, those problems are rare