When I was still in high school - I used to ride my three-speed every day. I pulled away from a stop light and got up to speed in a hurry. Just then a car passed me, and seeing a hitchhiker, immediately turned into a driveway to pick him up. I hit the side of the VW Beetle at the rear wheel. Hitchhiker came running up to me - the girl driving the Bug never even knew she hit me. I got the handlebar stem right on the sternum, tearing the cartilage holding the ribs. Hurt to breathe for months afterwards.
Worst non-accident experience while riding was going on a charity ride of 90 miles - on a cool Spring day. Again, I was still in high school, but at least now I had my first road bike - a heavy-as-a-tank Fuji Special Tourer. Weather forecast was to be partly cloudy and in the low-mid 50s, so I had dressed accordingly. However, a non-forecast cold soaking rain came up around mile 40 and didn't let up. Temps never got above mid 40s, and I was soaked to the skin. When I finished the ride, I literally had to pry my fingers off the handlebars. I had ridden 12 miles to the start of this ride, but was too frozen to ride back home. I went into a restaurant, called my mother from a payphone to come and get me, and sat in the warm restaurant drinking hot chocolate, shivering uncontrollably.