I've had a broken chain once, but that was my fault for not putting the pin in properly. I had a broken spoke one time as well, but managed to get home with a slightly wobbly wheel. One other time one of the retain clips on my pedal broke, or rather came loose, so I had to ride home more or less unclipped on one side.

Other than that, and numerous flat tires, I've had no issues. I have a multi tool as well, but have never actually used it on the road.