Once on POTC, the person behind me went to grab the back of my seat during the small drop and scraped a couple of places on my back with her nails. I got off and was bleeding from the scratches.
At TL, my older son who was 13 at the time, had a much larger adult run into him during a wave and scraped his knee very badly. He has a scar from it to this day.
My younger son's neck was cut when he was 12 at the barber shop at MK last year. I took a photo right after it happened and sent it to my DH (who wasn't with us that day in the park) because I was surprised he was cut during a haircut. He didn't wiggle or move, he was just slightly cut. The next day, it was infected and the infection spread half way across his neck over the next few days. I kept putting Neosporin on it and it did nothing. He was treated at his doctor and given antibiotics. It went away within a couple of weeks and he has no scarring. I notified Disney and sent the photos of the initial cut and then the infection. We were offered to have his dr. visits paid, but I declined. I just wanted them to make sure that they cleaned their blades and were more careful. My DH and sons have all had multiple haircuts there and dozens over their lives and never been cut.
Several years ago we were eating dinner in Epcot in Italy, and I bit down on pistachio gelato and nearly cracked a tooth on what I thought was a hard nut. I looked and it was a chip of ceramic. I notified the manager and he said that a plate had cracked earlier near the gelato and it was a piece of the plate. He said they got rid of all of the gelato and gave us our meals for free. He gave me his card and said if I had any further issue with my teeth to call and they'd take care of it. Luckily I was fine.
I think based on the number of times we have been to Disney and all of the rides we have ridden, that we are quite lucky we have been safe and mostly injury free.